Results 111 to 120 of about 8,851 (211)

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  

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
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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
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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
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Normalized homoclinic solutions of discrete nonlocal double phase problems

Bulletin of Mathematical Sciences
The aim of this paper is to discuss the existence of normalized solutions to the following nonlocal double phase problems driving by the discrete fractional Laplacian: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] if [Formula: see text], [Formula: see text] if [Formula:
Mingqi Xiang, Yunfeng Ma, Miaomiao Yang
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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
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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.
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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
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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  

Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization. [PDF]

Proc Natl Acad Sci U S A, 2023
Pinsky T.
europepmc   +1 more source