In this paper, we study a class of singular fractional differential system with Riemann-Stieltjes integral boundary condition by constructing a new cone and using Leggett-Williams fixed point theorem. The existence of...In this paper, we study a class of singular fractional differential system with Riemann-Stieltjes integral boundary condition by constructing a new cone and using Leggett-Williams fixed point theorem. The existence of multiple positive solutions is obtained. An example is presented to illustrate our main results.展开更多
By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations wit...By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions.The results in this paper improve some known results.展开更多
In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q (1 〈 q 〈 2) with non-separated integral boundary conditions. Some new existence and uniqueness results a...In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q (1 〈 q 〈 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.展开更多
In this paper, a kind of singularly perturbed first-order differential equations with integral boundary condition are considered. With the method of boundary layer function and the Banach fixed-point theorem, the unif...In this paper, a kind of singularly perturbed first-order differential equations with integral boundary condition are considered. With the method of boundary layer function and the Banach fixed-point theorem, the uniformly valid asymptotic solution of the original problem is obtained.展开更多
A singularly perturbed second-order semilinear differential equation with integral boundary conditions is considered. By the method of boundary functions, the conditions under which there exists an internal transition...A singularly perturbed second-order semilinear differential equation with integral boundary conditions is considered. By the method of boundary functions, the conditions under which there exists an internal transition layer for the original problem are established. The existence of spike-type solution is obtained by smoothly connecting the solutions of left and right associated problems, and the asymptotic expansion of the spike-type solution is also presented.展开更多
In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate pa...In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.展开更多
In this article, we discuss the existence and uniqueness of solutions for a coupled two-parameter system of sequential fractional integro-differential equations supplemented with nonlocal integro-multipoint boundary c...In this article, we discuss the existence and uniqueness of solutions for a coupled two-parameter system of sequential fractional integro-differential equations supplemented with nonlocal integro-multipoint boundary conditions. The standard tools of the fixed-point theory are employed to obtain the main results. We emphasize that our results are not only new in the given configuration, but also correspond to several new special cases for specific values of the parameters involved in the problem at hand.展开更多
An approximate artificial boundary condition based on a boundary integral equa- tion is designed for the vortex movements. Point vortex and cloud in cell methods are used in numerical simulation of vortex motions. The...An approximate artificial boundary condition based on a boundary integral equa- tion is designed for the vortex movements. Point vortex and cloud in cell methods are used in numerical simulation of vortex motions. The numerical experiments show that the ap- proximate artificial boundary condition is useful and su?ciently accurate in hydrodynamics.展开更多
Based on the Fourier transform, the analytical solution of boundary integral equations formulated for the complex velocity of a 2-D steady linear surface flow is derived. It has been found that before the radiation co...Based on the Fourier transform, the analytical solution of boundary integral equations formulated for the complex velocity of a 2-D steady linear surface flow is derived. It has been found that before the radiation condition is imposed,free waves appear both far upstream and downstream. In order to cancel the free waves in far upstream regions, the eigensolution of a specific eigenvalue, which satisfies the homogeneous boundary integral equation, is found and superposed to the analytical solution. An example, a submerged vortex, is used to demonstrate the derived analytical solution. Furthermore,an analytical approach to imposing the radiation condition in the numerical solution of boundary integral equations for 2-D steady linear wave problems is proposed.展开更多
Generalized impedance boundary conditions are employed to simplify the solution of the Sommerfeld half-space problem. An analytical expression is derived for the Hertz potential of a vertical electric dipole over the ...Generalized impedance boundary conditions are employed to simplify the solution of the Sommerfeld half-space problem. An analytical expression is derived for the Hertz potential of a vertical electric dipole over the earth’s surface, in which the earth is assumed to be a layered media or homogeneous dissipative half-space. A Sommerfeld type integral in the potential function is expressed as the sum of two parts: a zeroth order Hankel function and an absolutely convergent series of Bessel functions. In addition, two expressions in closed form are obtained as the far-field and near-field approximation of the present result.展开更多
Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic...Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.展开更多
In this paper,we consider the one dimensional third order p-Laplacian equation(Фp(u″))′+h(t)f(t,u(t))=0 with integral boundary conditions u(0)-αu′(0)=∫_(0)^(1) g1(s)u(s)ds,u(1)+βu′(1)=∫_(0)^(1)g2(s)u(s)ds,u″...In this paper,we consider the one dimensional third order p-Laplacian equation(Фp(u″))′+h(t)f(t,u(t))=0 with integral boundary conditions u(0)-αu′(0)=∫_(0)^(1) g1(s)u(s)ds,u(1)+βu′(1)=∫_(0)^(1)g2(s)u(s)ds,u″(0)=0.By using kernel functions and the Avery-Peterson fixed point theorem,we establish the existence of at least three positive solutions.展开更多
Based on the Guo-Krasnoselskii’s fixed-point theorem,the existence and multiplicity of positive solutions to a boundary value problem(BVP)with two integral boundary conditions{v(4)=f(s,v(s),v′(s),v〞(s)),s∈[0,1],v...Based on the Guo-Krasnoselskii’s fixed-point theorem,the existence and multiplicity of positive solutions to a boundary value problem(BVP)with two integral boundary conditions{v(4)=f(s,v(s),v′(s),v〞(s)),s∈[0,1],v′(1)=v′'′(1)=0,v(0)=∫10 g1(T)v(T)dT,v′′(0)=∫10 g2(T)v′′(T)dT}are obtained,where f,g1,g2 are all continuous.It generalizes the results of one positive solution to multiplicity and improves some results for integral BVPs.Moreover,some examples are also included to demonstrate our results as applications.展开更多
By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f(t,u) is non-increasing respect to u.
This paper presents a new analytical solution for the vibration response of a beamstiffened Mindlin plate having a completely free boundary condition by utilizing a finite cosine integral transform.In the solution,the...This paper presents a new analytical solution for the vibration response of a beamstiffened Mindlin plate having a completely free boundary condition by utilizing a finite cosine integral transform.In the solution,the unknown coupling force and moments at the beam/plate interface and the unknown modal constants from the integral transform are determined by the continuity and compatibility conditions at the interface as well as the boundary conditions.It provides an easily implemented tool for exploring complex edge value problems for a class of higher-order partial differential equations represented by fully free‐stiffened Mindlin thick plates.The validity of the model is evaluated by comparing the calculated free and forced vibration responses of the beam‐stiffened plate with those calculated using a beamstiffened thin plate and those from finite element analysis.展开更多
We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions which contain some positive c...We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions which contain some positive constants.展开更多
This paper focuses on nonlocal integral boundary value problems for elliptic differential-operator equations. Here given conditions guarantee that maximal regularity and Fredholmness in L_p spaces. These results are a...This paper focuses on nonlocal integral boundary value problems for elliptic differential-operator equations. Here given conditions guarantee that maximal regularity and Fredholmness in L_p spaces. These results are applied to the Cauchy problem for abstract parabolic equations, its infinite systems and boundary value problems for anisotropic partial differential equations in mixed L_p norm.展开更多
基金The University NSF (KJ2017A442,KJ2018A0452) of Anhui Provincial Education Departmentthe Foundation (2016XJGG13,2019XJZY02,2019XJSN03) of Suzhou University
文摘In this paper, we study a class of singular fractional differential system with Riemann-Stieltjes integral boundary condition by constructing a new cone and using Leggett-Williams fixed point theorem. The existence of multiple positive solutions is obtained. An example is presented to illustrate our main results.
基金SuppoSed by the NSF of Anhui Provincial Education Depaxtment(KJ2012A265,KJ2012B187)
文摘By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions.The results in this paper improve some known results.
文摘In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q (1 〈 q 〈 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.
基金supported by the National Natural Science Foundation of China (Grant No.10701023)and the E-Institutes of Shanghai Municipal Education Commission (Grant No.E03004)
文摘In this paper, a kind of singularly perturbed first-order differential equations with integral boundary condition are considered. With the method of boundary layer function and the Banach fixed-point theorem, the uniformly valid asymptotic solution of the original problem is obtained.
基金National Natural Science Foundation of China(No.10701023)the Fundamental Research Funds for the Central Universities,China+1 种基金E-Institutes of Shanghai Municipal Education Commission,China(No.E03004)Natural Science Foundation of Shanghai,China(No.10ZR1400100)
文摘A singularly perturbed second-order semilinear differential equation with integral boundary conditions is considered. By the method of boundary functions, the conditions under which there exists an internal transition layer for the original problem are established. The existence of spike-type solution is obtained by smoothly connecting the solutions of left and right associated problems, and the asymptotic expansion of the spike-type solution is also presented.
文摘In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.
文摘In this article, we discuss the existence and uniqueness of solutions for a coupled two-parameter system of sequential fractional integro-differential equations supplemented with nonlocal integro-multipoint boundary conditions. The standard tools of the fixed-point theory are employed to obtain the main results. We emphasize that our results are not only new in the given configuration, but also correspond to several new special cases for specific values of the parameters involved in the problem at hand.
文摘An approximate artificial boundary condition based on a boundary integral equa- tion is designed for the vortex movements. Point vortex and cloud in cell methods are used in numerical simulation of vortex motions. The numerical experiments show that the ap- proximate artificial boundary condition is useful and su?ciently accurate in hydrodynamics.
文摘Based on the Fourier transform, the analytical solution of boundary integral equations formulated for the complex velocity of a 2-D steady linear surface flow is derived. It has been found that before the radiation condition is imposed,free waves appear both far upstream and downstream. In order to cancel the free waves in far upstream regions, the eigensolution of a specific eigenvalue, which satisfies the homogeneous boundary integral equation, is found and superposed to the analytical solution. An example, a submerged vortex, is used to demonstrate the derived analytical solution. Furthermore,an analytical approach to imposing the radiation condition in the numerical solution of boundary integral equations for 2-D steady linear wave problems is proposed.
文摘Generalized impedance boundary conditions are employed to simplify the solution of the Sommerfeld half-space problem. An analytical expression is derived for the Hertz potential of a vertical electric dipole over the earth’s surface, in which the earth is assumed to be a layered media or homogeneous dissipative half-space. A Sommerfeld type integral in the potential function is expressed as the sum of two parts: a zeroth order Hankel function and an absolutely convergent series of Bessel functions. In addition, two expressions in closed form are obtained as the far-field and near-field approximation of the present result.
基金This project is supported by National Natural Science Foundation of China(No.50175031).
文摘Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.
基金supported by the National Natural Science Foundation of China(No.12071491)。
文摘In this paper,we consider the one dimensional third order p-Laplacian equation(Фp(u″))′+h(t)f(t,u(t))=0 with integral boundary conditions u(0)-αu′(0)=∫_(0)^(1) g1(s)u(s)ds,u(1)+βu′(1)=∫_(0)^(1)g2(s)u(s)ds,u″(0)=0.By using kernel functions and the Avery-Peterson fixed point theorem,we establish the existence of at least three positive solutions.
文摘Based on the Guo-Krasnoselskii’s fixed-point theorem,the existence and multiplicity of positive solutions to a boundary value problem(BVP)with two integral boundary conditions{v(4)=f(s,v(s),v′(s),v〞(s)),s∈[0,1],v′(1)=v′'′(1)=0,v(0)=∫10 g1(T)v(T)dT,v′′(0)=∫10 g2(T)v′′(T)dT}are obtained,where f,g1,g2 are all continuous.It generalizes the results of one positive solution to multiplicity and improves some results for integral BVPs.Moreover,some examples are also included to demonstrate our results as applications.
基金supported by Program for Scientific research innovation team in Colleges and universities of Shandong Provincethe Doctoral Program Foundation of Education Ministry of China(20133705110003)+1 种基金the Natural Science Foundation of Shandong Province of China(ZR2014AM007)the National Natural Science Foundation of China(11571197)
文摘By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f(t,u) is non-increasing respect to u.
基金The financial support from the Qingdao Postdoctoral Applied Research Program(No.862205040040)for this work is gratefully acknowledged.
文摘This paper presents a new analytical solution for the vibration response of a beamstiffened Mindlin plate having a completely free boundary condition by utilizing a finite cosine integral transform.In the solution,the unknown coupling force and moments at the beam/plate interface and the unknown modal constants from the integral transform are determined by the continuity and compatibility conditions at the interface as well as the boundary conditions.It provides an easily implemented tool for exploring complex edge value problems for a class of higher-order partial differential equations represented by fully free‐stiffened Mindlin thick plates.The validity of the model is evaluated by comparing the calculated free and forced vibration responses of the beam‐stiffened plate with those calculated using a beamstiffened thin plate and those from finite element analysis.
文摘We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions which contain some positive constants.
文摘This paper focuses on nonlocal integral boundary value problems for elliptic differential-operator equations. Here given conditions guarantee that maximal regularity and Fredholmness in L_p spaces. These results are applied to the Cauchy problem for abstract parabolic equations, its infinite systems and boundary value problems for anisotropic partial differential equations in mixed L_p norm.