Homoclinic orbits for a class of symmetric Hamiltonian systems
Electronic Journal of Differential Equations, 1994 of Hamiltonian systems that are symmetric with respect to independent variable (time). For the scalar case we prove existence and uniqueness of a positive homoclinic solution. For the system case we prove existence of symmetric homoclinic orbits.
Philip Korman, Alan C. Lazer
doaj +2 more sources
Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations [PDF]
Advances in Difference Equations, 2010 By using the critical point theory, we establish some existence criteria to guarantee that the nonlinear difference equation has at least one homoclinic solution, where , and is non periodic in .
Chen Peng, Tang XH
doaj +4 more sources
New homoclinic solutions for a class of second-order Hamiltonian systems with a mixed condition
Boundary Value Problems, 2018 In this paper, we introduce a new mixed condition to obtain a new compact embedding theorem. Under this theorem, we study the existence and multiplicity of nontrivial homoclinic solutions for a class of second-order Hamiltonian systems with variable ...
Xuefeng Li, Jin Jia
doaj +2 more sources
Multiplicity of Homoclinic Solutions for a Class of Nonperiodic Fourth-Order Differential Equations with General Perturbation [PDF]
Abstract and Applied Analysis, 2014 In this paper, we investigate a class of nonperiodic fourth-order differential equations with general perturbation. By using the mountain pass theorem and the Ekeland variational principle, we obtain that such equations possess two homoclinic solutions ...
Liu Yang
doaj +2 more sources
Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems [PDF]
Abstract and Applied Analysis, 2013 We give several sufficient conditions under which the first-order nonlinear discrete Hamiltonian system Δx(n)=α(n)x(n+1)+β(n)|y(n)|μ-2y(n),Δy(n)=-γ(n)|x(n+1)|ν-2x(n+1)-α(n)y(n) has no solution (x(n),y(n)) satisfying condition ...
Xiaoping Wang
doaj +4 more sources
Existence and Uniqueness of Homoclinic Solution for a Class of Nonlinear Second-Order Differential Equations [PDF]
Journal of Applied Mathematics, 2012 The authors study the existence and uniqueness of a set with 2kT-periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a ...
Lijuan Chen, Shiping Lu
doaj +2 more sources
Abstract and Applied Analysis, 2014 By using critical point theory, we obtain a new sufficient condition on the existence of homoclinic solutions of a class of nonperiodic discrete nonlinear systems in infinite lattices. The classical Ambrosetti-Rabinowitz superlinear condition is improved
Genghong Lin, Zhan Zhou
doaj +2 more sources
Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge. [PDF]
Quant BiolAbstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Zhang P, Gao T, Guo J, Duan J.
europepmc +2 more sources
Positive Homoclinic Solutions for a Class of Second Order Differential Equations
Journal of Mathematical Analysis and Applications, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Grossinho, Maria do Rosário +2 more
core +4 more sources
Existence of homoclinic orbits for a class of nonlinear functional difference equations
Electronic Journal of Differential Equations, 2016 By using critical point theory, we prove the existence of a nontrivial homoclinic orbit for a class of nonlinear functional difference equations. Our conditions on the nonlinear term do not need to satisfy the well-known global Ambrosetti-Rabinowitz ...
Xia Liu, Tao Zhou, Haiping Shi
doaj +1 more source