In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ...In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.展开更多
This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is pres...This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.展开更多
The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the ...The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, it is proved that the scheme converges uniformly to the solution of differential equation with order one.展开更多
We apply the distributional derivative to study the existence of solutions of the second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The distributional Henstock-Kurz...We apply the distributional derivative to study the existence of solutions of the second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The distributional Henstock-Kurzweil integral is a general intergral, which contains the Lebesgue and Henstock-Kurzweil integrals. And the distributional derivative includes ordinary derivatives and approximate derivatives. By using the method of upper and lower solutions and a fixed point theorem, we achieve some results which are the generalizations of some previous results in the literatures.展开更多
Mathematical models of propellers were created that investigate the influence of periodic boundary conditions on predictions of a propeller's performance.Thrust and torque coefficients corresponding to different a...Mathematical models of propellers were created that investigate the influence of periodic boundary conditions on predictions of a propeller's performance.Thrust and torque coefficients corresponding to different advance coefficients of DTMB 4119, 4382, and 4384 propellers were calculated.The pressure coefficient distribution of the DTMB 4119 propeller at different sections was also physically tested.Comparisons indicated good agreement between the results of experiments and the simulation.It showed that the periodic boundary condition can be used to rationally predict the open water performance of a propeller.By analyzing the three established modes for the computation, it was shown that using the spline curve method to divide the grids can meet the calculation's demands for precision better than using the rake cutting method.展开更多
Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish...Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results. Results and Conclusion The results of the existence of maximal and minimal solutions of the periodic boundary value problem for functional differential equations with impulses are obtained.展开更多
We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the con...We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.展开更多
By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential ...By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential equations in Banach spaces is proved.展开更多
We proposed a kind of doubly periodic Riemann boundary value problem on two parallel curves. By using the method of complex functions, we investigated the method for solving this kind of doubly periodic Riemann bounda...We proposed a kind of doubly periodic Riemann boundary value problem on two parallel curves. By using the method of complex functions, we investigated the method for solving this kind of doubly periodic Riemann boundary value problem of normal type and gave the general solutions and the solvable conditions for it.展开更多
In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by me...In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.展开更多
The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the ...The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, it is proved that the scheme converges uniformly to the solution of differential equation with order one.展开更多
Direct numerical simulation(DNS) of gas–solid flow at high resolution has been carried out by coupling the lattice Boltzmann method(LBM) for gas flow and the discrete element method(DEM) for solid particles. However,...Direct numerical simulation(DNS) of gas–solid flow at high resolution has been carried out by coupling the lattice Boltzmann method(LBM) for gas flow and the discrete element method(DEM) for solid particles. However,the body force periodic boundary condition(FPBC) commonly used to cut down the huge computational cost of such simulation has faced accuracy concerns. In this study, a novel two-region periodic boundary condition(TPBC) is presented to remedy this problem, with the flow driven in the region with body force and freely evolving in the other region. With simulation cases for simple circulating fluidized bed risers, the validity and advantages of TPBC are demonstrated with more reasonable heterogeneity of the particle distribution as compared to the corresponding case with FPBC.展开更多
We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, ...We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.展开更多
A 1.5-layer quasi-geostrophic reduced gravity model is used to study the hysteresis of a periodic or leaking western boundary current(WBC) flowing by a gap. When the periods of the WBC variations are much longer than ...A 1.5-layer quasi-geostrophic reduced gravity model is used to study the hysteresis of a periodic or leaking western boundary current(WBC) flowing by a gap. When the periods of the WBC variations are much longer than the Rossby adjustment time scales of the circulation in the vicinity of the gap, the Hopf bifurcations during the Reincrease and Re-decrease loops are delayed to produce a new domain of hysteresis of the Reynolds numbers, and the critical Reynolds numbers of the WBC regime transitions change significantly, with the domain of the hysteresis Reynolds number larger for shorter periodic forcing. When the periods of the WBC variations are comparable to those of the Rossby adjustment time scales of the circulation in the vicinity of the gap, the WBC path inside the gap becomes periodic without hysteresis. The intrusion of the WBC into the western basin generally gets smaller as the period decreases. In addition, the partial leakage of the WBC transport through the gap into the western basin is found to have significant impact on the hysteresis loop of the WBC path when the leaked transport is larger than 1/2 of the WBC. Both the intrusion extent and the critical Reynolds numbers of the WBC regime transition are changed, and the larger the throughflow transport, the larger the change.展开更多
We have studied the compound periodic boundary problem in the upper halfplane above the real axis. Under proper conditions, we obtain a periodic and sectionallyholo-morphic function in the upper half plane. In additio...We have studied the compound periodic boundary problem in the upper halfplane above the real axis. Under proper conditions, we obtain a periodic and sectionallyholo-morphic function in the upper half plane. In addition, we have also solved the compoundboundary problem with discontinuities of the first kind of the coefficients in the Hilbertcondition.展开更多
In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular ...In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h2).展开更多
This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch curre...This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch current excited by plane wave. Impedance matrix elements are computed by using fast Fourier transform(FFT), and reduced equation is solved by using diakoptic technique. Consequently, the computing time is reduced significantly. The convergence property of simulating open structure by using PBC and the comparison of the computer time between using PBC and usual absorbing boundary condition (ABC) show the validity of the method proposed in this paper. Finally, the resonant frequency of a microstrip patch is computed. The numerical results obtained are in good agreement with those published.展开更多
In this paper, we present and study a kind of Riemann boundary value problem of non-normal type for analytic functions on two parallel curves. Making use of the method of complex functions, we give the method for solv...In this paper, we present and study a kind of Riemann boundary value problem of non-normal type for analytic functions on two parallel curves. Making use of the method of complex functions, we give the method for solving this kind of doubly periodic Riemann boundary value problem of non-normal type and obtain the explicit expressions of solutions and the solvable conditions for it.展开更多
In this paper, the properties of solution of periodic boundary value problem for second-order impulsive integro-differential equation are discussed. Using the iterative analysis method, the existence and uniqueness of...In this paper, the properties of solution of periodic boundary value problem for second-order impulsive integro-differential equation are discussed. Using the iterative analysis method, the existence and uniqueness of periodic solution and the sufficient condition for uniform stability of trivial solution are obtained, which extend the previous results on integro-differential equation in periodic boundary value problem.展开更多
基金Supported by NSFC(11326127,11101335)NWNULKQN-11-23the Fundamental Research Funds for the Gansu Universities
文摘In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.
基金Supported by the National Natural Science Foundation of China (10571050 10871062)Hunan Provincial Innovation Foundation For Postgraduate
文摘This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.
文摘The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, it is proved that the scheme converges uniformly to the solution of differential equation with order one.
文摘We apply the distributional derivative to study the existence of solutions of the second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The distributional Henstock-Kurzweil integral is a general intergral, which contains the Lebesgue and Henstock-Kurzweil integrals. And the distributional derivative includes ordinary derivatives and approximate derivatives. By using the method of upper and lower solutions and a fixed point theorem, we achieve some results which are the generalizations of some previous results in the literatures.
基金Supported by the National Natural Science Foundation of China under Grant No.10702016
文摘Mathematical models of propellers were created that investigate the influence of periodic boundary conditions on predictions of a propeller's performance.Thrust and torque coefficients corresponding to different advance coefficients of DTMB 4119, 4382, and 4384 propellers were calculated.The pressure coefficient distribution of the DTMB 4119 propeller at different sections was also physically tested.Comparisons indicated good agreement between the results of experiments and the simulation.It showed that the periodic boundary condition can be used to rationally predict the open water performance of a propeller.By analyzing the three established modes for the computation, it was shown that using the spline curve method to divide the grids can meet the calculation's demands for precision better than using the rake cutting method.
文摘Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results. Results and Conclusion The results of the existence of maximal and minimal solutions of the periodic boundary value problem for functional differential equations with impulses are obtained.
基金supported by the NSFC(12071413)the Guangxi Natural Sci-ence Foundation(2023GXNSFAA026085)the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECH。
文摘We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.
基金theNaturalScienceFoundationofEducationalCommitteeofHainanProvince China
文摘By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential equations in Banach spaces is proved.
文摘We proposed a kind of doubly periodic Riemann boundary value problem on two parallel curves. By using the method of complex functions, we investigated the method for solving this kind of doubly periodic Riemann boundary value problem of normal type and gave the general solutions and the solvable conditions for it.
文摘In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.
文摘The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, it is proved that the scheme converges uniformly to the solution of differential equation with order one.
基金Supported by the National Natural Science Foundation of China(21821005,91834303)Science Challenge Project(TZ2016001)+1 种基金the Key Research Program of Frontier Science of the Chinese Academy of Sciences(QYZDJ-SSW-JSC029)the Strategic Priority Research Program of the CAS(XDA21030700).
文摘Direct numerical simulation(DNS) of gas–solid flow at high resolution has been carried out by coupling the lattice Boltzmann method(LBM) for gas flow and the discrete element method(DEM) for solid particles. However,the body force periodic boundary condition(FPBC) commonly used to cut down the huge computational cost of such simulation has faced accuracy concerns. In this study, a novel two-region periodic boundary condition(TPBC) is presented to remedy this problem, with the flow driven in the region with body force and freely evolving in the other region. With simulation cases for simple circulating fluidized bed risers, the validity and advantages of TPBC are demonstrated with more reasonable heterogeneity of the particle distribution as compared to the corresponding case with FPBC.
基金supported by the National Natural Science Foundation of China(11371141 and 11871218)Science and Technology Commission of Shanghai Municipality(STCSM)under Grant No.18dz2271000
文摘We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.
基金The National Program on Global Change and Air-Sea Interaction under contract Nos GASI-03-01-01-05,GASIIPOVAI-01-02,GASI-IPOVAI-02,GASI-IPOVAI-03,GASI-IPOVAI-01-05 and GASI-03-01-01-02the National Natural Science Foundation of China(NSFC)under contract Nos 41421005,41720104008,41476025,41376038 and 41876025+4 种基金the National Natural Science Foundation of China(NSFC)-Shandong Joint Fund for Marine Science Research Centers of China under contract Nos U1606402 and U1606405the CAS Strategic Priority Project under contract No.XDA11010205the Scientific and Technological Innovation Project of Qingdao National Laboratory for Marine Science and Technology under contract No.2016ASKJ04the National Science and Technology Major Project under contract No.2016ZX05057015the Open Fund of Shandong Provincial Key Laboratory of Marine Ecology and Environment & Disaster Prevention and Mitigation under contract No.201701
文摘A 1.5-layer quasi-geostrophic reduced gravity model is used to study the hysteresis of a periodic or leaking western boundary current(WBC) flowing by a gap. When the periods of the WBC variations are much longer than the Rossby adjustment time scales of the circulation in the vicinity of the gap, the Hopf bifurcations during the Reincrease and Re-decrease loops are delayed to produce a new domain of hysteresis of the Reynolds numbers, and the critical Reynolds numbers of the WBC regime transitions change significantly, with the domain of the hysteresis Reynolds number larger for shorter periodic forcing. When the periods of the WBC variations are comparable to those of the Rossby adjustment time scales of the circulation in the vicinity of the gap, the WBC path inside the gap becomes periodic without hysteresis. The intrusion of the WBC into the western basin generally gets smaller as the period decreases. In addition, the partial leakage of the WBC transport through the gap into the western basin is found to have significant impact on the hysteresis loop of the WBC path when the leaked transport is larger than 1/2 of the WBC. Both the intrusion extent and the critical Reynolds numbers of the WBC regime transition are changed, and the larger the throughflow transport, the larger the change.
基金Supported by the National Natural Science Foundations of China (19971064)
文摘We have studied the compound periodic boundary problem in the upper halfplane above the real axis. Under proper conditions, we obtain a periodic and sectionallyholo-morphic function in the upper half plane. In addition, we have also solved the compoundboundary problem with discontinuities of the first kind of the coefficients in the Hilbertcondition.
基金This work is supported by the National Fujian Province Nature Science Research Funds
文摘In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h2).
基金Supported by the National Natural Science Foundation of China
文摘This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch current excited by plane wave. Impedance matrix elements are computed by using fast Fourier transform(FFT), and reduced equation is solved by using diakoptic technique. Consequently, the computing time is reduced significantly. The convergence property of simulating open structure by using PBC and the comparison of the computer time between using PBC and usual absorbing boundary condition (ABC) show the validity of the method proposed in this paper. Finally, the resonant frequency of a microstrip patch is computed. The numerical results obtained are in good agreement with those published.
文摘In this paper, we present and study a kind of Riemann boundary value problem of non-normal type for analytic functions on two parallel curves. Making use of the method of complex functions, we give the method for solving this kind of doubly periodic Riemann boundary value problem of non-normal type and obtain the explicit expressions of solutions and the solvable conditions for it.
基金Supported by the Natural Science Foundation of Hainan Province（112006） Supported by the Natural Science Foundation of Department of Education of Hainan Province（Hjkj2013-47） Supported by the National Basic Research Program of China（973Program, 2011CB710600）
文摘In this paper, the properties of solution of periodic boundary value problem for second-order impulsive integro-differential equation are discussed. Using the iterative analysis method, the existence and uniqueness of periodic solution and the sufficient condition for uniform stability of trivial solution are obtained, which extend the previous results on integro-differential equation in periodic boundary value problem.
