Results 101 to 110 of about 3,396,163 (214)
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 systemΔx(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 condition0<∑n=-∞+∞[|x(n)|ν+(1+β(n))|y(n)|μ]<+∞, whereμ,ν>1and1/μ+1/ν=1andα(n),β(n),andγ(n)are real-valued functions defined onℤ.
openaire +4 more sources
Probabilistic approach to homoclinic chaos
, 1994 Three-dimensional systems possessing a homoclinic orbit associated to a saddle focus with eigenvalues ρ{variant}±iω, -λ and giving rise to homoclinic chaos when the Shil'nikov condition ρ{variant}
Nicolis, Grégoire, Daems, David
core +1 more source
Homoclinic solutions for second-order nonlinear difference equations with Jacobi operators
Electronic Journal of Differential Equations, 2017 We obtain sufficient conditions for the existence of a nontrivial homoclinic solution to a second-order nonlinear difference equation with Jacobi operator. To do this, we use variational methods and critical point theory.
Fei Xia
doaj
Homoclinic solutions for second-order Hamiltonian systems with periodic potential
Boundary Value Problems, 2018 In this paper, we study the second-order Hamiltonian systems u¨−L(t)u+∇W(t,u)=0,t∈R, $$ \ddot{u}-L(t)u+\nabla W(t,u)=0,\quad t\in \mathbb{R}, $$ where L∈C(R,RN×N) $L\in C(\mathbb{R},\mathbb{R}^{N\times N})$ is a T-periodic and positive definite matrix ...
Yiwei Ye
doaj +1 more source
Homoclinics for strongly indefinite almost periodic second order Hamiltonian systems
Advances in Nonlinear Analysis, 2017 Under certain assumptions, we prove the existence of homoclinic solutions for almost periodic second order Hamiltonian systems in the strongly indefinite case.
Pankov Alexander
doaj +1 more source
Homoclinic trajectories of non-autonomous maps
, 2011 Hüls T. Homoclinic trajectories of non-autonomous maps. Journal of Difference Equations and Applications. 2011;17(1):9-31.For non-autonomous difference equations of the form[image omitted]we consider homoclinic trajectories.
Thorsten Hüls, Hüls, Thorsten
core +1 more source
Multibump solutions for an almost periodically forced singular Hamiltonian system
Electronic Journal of Differential Equations, 1995 existence of so-called multibump homoclinic solutions for a family of singular Hamiltonian systems in $R^2$ which are subjected to almost periodic forcing in time.
Paul H. Rabinowitz
doaj
Existence of homoclinic solutions for Hamiltonian systems
Advances in Differential Equations, 2002 Using variational methods, the existence of homoclinic solutions is shown for the Hamiltonian system \(Ju'(x)+Mu(x)-\nabla_uF(x,u(x))=\lambda u(x)\), where \(u : \mathbb{R}\to \mathbb{R}^{2N}\), \(J\), \(M\) are matrices such that \(J=-J^T=-J^{-1}\), \(M^T=M\) and \(F\) is a Carathéodory nonlinearity satisfying addition properties.
openaire +3 more sources
Infinitely Many Homoclinic Orbits for Hamiltonian Systems with Group Symmetries
, 2013 [[abstract]]This paper deals via variational methods with the existence of infinitely many homoclinic orbits for a class of the first-order time-dependent Hamiltonian systems ż = JHz(t, z) without any periodicity assumption on H, providing that H(t, z ...
Lee, Cheng
core
Multiple homoclinic solutions for superquadratic Hamiltonian systems
Electronic Journal of Differential Equations, 2016 In this article we study the existence of infinitely many homoclinic solutions for a class of second-order Hamiltonian systems $$ \ddot{u}-L(t)u+W_u(t,u)=0, \quad \forall t\in\mathbb{R}, $$ where L is not required to be either uniformly positive ...
Wei Jiang, Qingye Zhang
doaj