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ON THE STABILITY OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC DIFFERENTIAL EQUATIONS
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作者 Maoan HAN Yan YE 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1524-1535,共12页
In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic sol... In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications. 展开更多
关键词 periodic solution Poincarémap periodic equation stability
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Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation
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作者 Dahe Feng Jibin Li Airen Zhou 《Applied Mathematics》 2024年第8期543-567,共25页
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ... For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation. 展开更多
关键词 (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation BIFURCATIONS Phase Portrait Analytical Periodic Wave Solution Periodic Cusp Wave Solution
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Dynamics and Exact Solutions of (1 + 1)-Dimensional Generalized Boussinesq Equation with Time-Space Dispersion Term
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作者 Dahe Feng Jibin Li Jianjun Jiao 《Journal of Applied Mathematics and Physics》 2024年第8期2723-2737,共15页
We study exact solutions to (1 + 1)-dimensional generalized Boussinesq equation with time-space dispersion term by making use of improved sub-equation method, and analyse the dynamical behavior and exact solutions of ... We study exact solutions to (1 + 1)-dimensional generalized Boussinesq equation with time-space dispersion term by making use of improved sub-equation method, and analyse the dynamical behavior and exact solutions of the sub-equation after constructing the nonlinear transformation and constraint conditions. Accordingly, we obtain twenty families of exact solutions such as analytical and singular solitons and singular periodic waves. In addition, we discuss the impact of system parameters on wave propagation. 展开更多
关键词 Generalized Boussinesq Equation Improved Sub-Equation Method BIFURCATION Soliton Solution Periodic Solution
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Diversity of Rogue Wave Solutions to the (1+1)-Dimensional Boussinesq Equation
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作者 Xiaoming Wang Jingjie Huang 《Journal of Applied Mathematics and Physics》 2024年第2期458-467,共10页
A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics ... A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β. 展开更多
关键词 Boussinesq Equation Rogue wave periodically Homoclinic Solution Spatiotemporal Structure
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TIME PERIODIC SOLUTIONS TO THE EVOLUTIONARY OSEEN MODEL FOR A GENERALIZED NEWTONIAN INCOMPRESSIBLE FLUID
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作者 岑金夏 Stanislaw MIGóRSKI +1 位作者 Emilio VILCHES 曾生达 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1645-1667,共23页
In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the mode... In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity field.Then,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is investigated.Under mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are proven.Furthermore,a uniqueness theorem for the abstract inequality is established by using a monotonicity argument.Finally,we employ the theoretical results to examine the nonstationary Oseen model. 展开更多
关键词 nonstationary Oseen model Newtonian incompressible fluid hemivariational inequality periodic solution generalized subgradient
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Existence of Periodic Solutions for Higher Order Autonomous Birkhoff Systems 被引量:3
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作者 陈向炜 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 2000年第2期125-130,共6页
Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkho... Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkhoff systems, the character of the characteristic roots of the Fréchet derivative C was obtained. Furthermore the existence theorem of periodic solutions was obtained by using Liapunov center theorem, and an example was presented to illustrate the results. 展开更多
关键词 Birkhoff system Liapunov center theorem periodic solution
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On the Existence of Periodic Solutions of a Class Nonlinear Differential Systems 被引量:1
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作者 李林 徐琛梅 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第4期69-77,共9页
One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equati... One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equations the main results are obtained. 展开更多
关键词 differential system periodic solutions BOUNDEDNESS
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Exponential stability and existence of periodic solutions for a class of recurrent neural networks with delays 被引量:1
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作者 戴志娟 《Journal of Southeast University(English Edition)》 EI CAS 2006年第2期286-293,共8页
Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays (RNNs) are studied. By employing the inequality α∏k=1^m ... Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays (RNNs) are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r+1/rα^r(α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications. 展开更多
关键词 recurrent neural network global exponential stability periodic solution delay HOMEOMORPHISM Lyapunov function
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Existence of Periodic Solutions for Generalized Liénard-Typed Functional Differential Equations
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作者 贺小明 葛渭高 单文锐 《Journal of Beijing Institute of Technology》 EI CAS 2002年第3期325-328,共4页
The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are ... The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended. 展开更多
关键词 functional differential equation periodic solution coincidence degree
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Existence of Periodic Solutions of Nonlinear Neutral Differential Equation with Deviating Argument
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作者 任景莉 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2002年第4期439-443,共5页
Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set ... Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique. 展开更多
关键词 neutral delay differential equation periodic solution Fredholm operator k-set contractive operator
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Quadratic integrability of solutions based on a class of delayed systems
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作者 计国君 《Journal of Southeast University(English Edition)》 EI CAS 2007年第4期630-638,共9页
Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function,... Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function, the Lyapunov functional or the Beuman-Bihari inequality, and some sufficient conditions based on those properties are given. Finally, the conclusions are applied to over-voltage models based on three-phase nonsynchronous closing of switches appearing in the power systems, the results in accord with the background physical meaning are obtained. And all the conditions of the conclusions are easy to validate, so the conclusions have definite theoretical meaning and are easy to apply in practice. 展开更多
关键词 nonlinear delayed system quadratic integrability periodic solution oscillatory solution OVERVOLTAGE
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Existence of Many and Infinitely Many Periodic Solutions for Some Types of Differential Delay Equations
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作者 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 1993年第1期5-14,共10页
J.Kaplan and J.Yorke's method is extended to establish the exis- tence of many and infinitely many periodic solutions for the DDEs (t) =±f(x(t-1))±f(x(t-2))and (t)=±f(x(t-1).
关键词 difference differential equation periodic solution SYMMETRY
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EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS 被引量:23
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作者 LuShiping GeWeigao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第4期382-390,共9页
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(... By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))]. 展开更多
关键词 positive periodic solution abstract continuation theorem neutral functional differential equation.
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EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR VOLTERRA INTERGO-DIFFERENTIAL EQUATIONS 被引量:8
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作者 蒋达清 魏俊杰 《Acta Mathematica Scientia》 SCIE CSCD 2001年第4期553-560,共8页
This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems ... This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results. 展开更多
关键词 Volterra integro-differential equation EXISTENCE positive periodic solution fixed point theorem
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Infinitely many periodic solutions for second-order Hamiltonian systems
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作者 尹翠翠 张福保 黄成山 《Journal of Southeast University(English Edition)》 EI CAS 2009年第4期549-551,共3页
The existence of high energy periodic solutions for the second-order Hamiltonian system -ü(t)+A(t)u(t)=▽F(t,u(t)) with convex and concave nonlinearities is studied, where F(t, u) = F1(t,u)+F2(t,... The existence of high energy periodic solutions for the second-order Hamiltonian system -ü(t)+A(t)u(t)=▽F(t,u(t)) with convex and concave nonlinearities is studied, where F(t, u) = F1(t,u)+F2(t,u). Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory. 展开更多
关键词 variant fountain theorem second-order Hamiltonian system infinitely periodic solutions even functional
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EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN 被引量:4
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作者 葛斌 薛小平 周庆梅 《Acta Mathematica Scientia》 SCIE CSCD 2011年第5期1786-1802,共17页
We study a nonlinear periodic problem driven by the p(t)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally L... We study a nonlinear periodic problem driven by the p(t)-Laplacian and having a nonsmooth potential (hemivariational inequalities). Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic. 展开更多
关键词 p(t)-Laplacian periodic solution variable exponent Sobolev space minimax principle generalized subdifferential local linking reduction method
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Existence of two periodic solutions of a ratio-dependent Holling-Taner model with infinite delay and prey harvest 被引量:5
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作者 TIAN De-sheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第2期136-142,共7页
This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions fo... This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions for the existence of at least two positive periodic solutions of this model is established. 展开更多
关键词 Holling-Taner model RATIO-DEPENDENT HARVEST periodic solution coincidence degree.
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Periodic Solutions of Mixed Type p-Laplacian Equations with Deviating Arguments 被引量:5
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作者 WANG Xiao-ming 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第2期177-182,共6页
Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,... Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results. 展开更多
关键词 P-LAPLACIAN periodic solutions mixed type deviating argument Man’asevichMawhin continuation theorem
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A Series of Exact Solutions of (2+l)-Dimensional CDGKS Equation 被引量:5
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作者 YANG Zong-Hang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第5X期807-811,共5页
An algebraic method with symbolic computation is devised to uniformly construct a series of exact solutions of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawda equation. The solutions obtained in this paper i... An algebraic method with symbolic computation is devised to uniformly construct a series of exact solutions of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawda equation. The solutions obtained in this paper include solitary wave solutions, rational solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic solutions. Among them, the Jacobi periodic solutions exactly degenerate to the solutions at a certain limit condition. Compared with most existing tanh method, the method used here can give new and more general solutions. More importantly, this method provides a guldeline to classifj, the various types of the solution according to some parameters. 展开更多
关键词 CDGKS equations solitary wave solution Jacobi and Weierstrass periodic wave solution algebraic method
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New Periodic Wave Solutions to Generalized Klein-Gordon and Benjamin Equations 被引量:5
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作者 WU Guo-Jiang HAN Jia-Hua ZHANG Wen-Liang ZHANG Miao WANG Jun-Mao 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第5X期815-818,共4页
By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for general... By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for generalized Klein-Cordon equation and Benjamin equation, which cannot be found in previous work. This method also can be used to find new periodic wave solutions of other nonlinear evolution equations. 展开更多
关键词 auxiliary equation method extended mapping method nonlinear evolution equations periodic wave solutions
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