Results 81 to 90 of about 636 (179)

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

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

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  

Homoclinic solutions in periodic partial difference equations

Advances in Nonlinear Analysis
By using critical point theory in combination with periodic approximations, we obtain novel sufficient conditions for the existence of nontrivial homoclinic solutions for a class of periodic partial difference equations with sign-changing mixed ...
Mei Peng, Zhou Zhan, Yu Jianshe
doaj   +1 more source

Homoclinics for singular strong force Lagrangian systems

Advances in Nonlinear Analysis, 2019
We study the existence of homoclinic solutions for a class of Lagrangian systems ddt$\begin{array}{} \frac{d}{dt} \end{array} $(∇Φ(u̇(t))) + ∇uV(t, u(t)) = 0, where t ∈ ℝ, Φ : ℝ2 → [0, ∞) is a G-function in the sense of Trudinger, V : ℝ × (ℝ2 ∖ {ξ}) → ℝ ...
Izydorek Marek, Janczewska Joanna, Mawhin Jean   +2 more
doaj   +1 more source

The Existence of Transverse Homoclinic Solutions for Higher Order Equations

Journal of Differential Equations, 1996
Parametrized differential equations of the form \(\dot x(t)=f(x(t),\mu,t)\), where \(x\in \mathbb{R}^n\), \(\mu\in \mathbb{R}^N\), are considered. It is assumed that \(f\) is of \(C^3\)-class, \(f(x,0,t)\) is independent of \(t\), for all sufficiently small \(|\mu|\), \(x=0\) is a hyperbolic equilibrium, \(f\) is periodic in \(t\), and there exists a ...
openaire   +1 more source

Homoclinic solution to zero of a non-autonomous, nonlinear, second order differential equation with quadratic growth on the derivative

Electronic Journal of Qualitative Theory of Differential Equations
This work aims to obtain a positive, smooth, even, and homoclinic to zero (i.e. zero at infinity) solution to a non-autonomous, second-order, nonlinear differential equation involving quadratic growth on the derivative.
Luiz Fernando Faria, Pablo Corrêa Junior   +1 more
doaj   +1 more source

Interfering solutions of a nonhomogeneous Hamiltonian system

Electronic Journal of Differential Equations, 2001
A Hamiltonian system is studied which has a term approaching a constant at an exponential rate at infinity . A minimax argument is used to show that the equation has a positive homoclinic solution.
Gregory S. Spradlin
doaj  

Multiple homoclinic solutions for indefinite second-order discrete Hamilton system with small perturbation

Electronic Journal of Differential Equations, 2015
In this article, we sutdy the multiplicity of homoclinic solutions to the perturbed second-order discrete Hamiltonian system $$ \Delta[p(n)\Delta u(n-1)]-L(n)u(n)+\nabla W(n,u(n))+\theta\nabla F(n,u(n))=0, $$ where L(n) and W(n,x) are neither ...
Liang Zhang, Xianhua Tang
doaj