Results 111 to 120 of about 8,918 (208)
Homoclinic Solutions for a Class of Hamiltonian Systems
Advanced Nonlinear Studies, 2004 Abstract We consider the first order Hamiltonian system q̇ = Hp(p, q), ṗ = −Hq(p, q), (HS) where p, q : ℝ → ℝN (N ≥ 3), H ∈ C1 (ℝN × ℝN \ {e}, ℝ ) and behaves roughly like
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On Shilnikov's scenario in 3D: Topological chaos for vectorfields of class $C^1$
Electronic Journal of Qualitative Theory of Differential EquationsShilnikov's scenario in $\mathbb{R}^3$ means that the equation $x'=V(x)\in\mathbb{R}^3$ with $V(0)=0$ has a homoclinic solution and the eigenvalues of $DV(0)$ are $u>0$ and $\sigma\pm i\mu$ with ...
Hans-Otto Walther
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Multiple homoclinic solutions for singular differential equations
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2010 The homoclinic bifurcations of ordinary differential equation under singular perturbations are considered. We use exponential dichotomy, Fredholm alternative and scales of Banach spaces to obtain various bifurcation manifolds with finite codimension in an appropriate infinite-dimensional space. When the perturbative term is taken from these bifurcation
Zhu, Changrong +2 more
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Advances in Difference Equations, 2017 In this paper, we investigate the existence and multiplicity of homoclinic solutions for a class of nonlinear difference systems involving classical ( ϕ 1 , ϕ 2 ) $(\phi_{1},\phi _{2})$ -Laplacian and a parameter: { Δ ( ρ 1 ( n − 1 ) ϕ 1 ( Δ u 1 ( n − 1 )
Xingyong Zhang +3 more
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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
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HOMOCLINIC SOLUTIONS OF DISCRETE NONLINEAR SYSTEMS VIA VARIATIONAL METHOD
Journal of Applied Analysis & Computation, 2019 Summary: Homoclinic solutions arise in various discrete models with variational structure, from discrete nonlinear Schrödinger equations to discrete Hamiltonian systems. In recent years, a lot of interesting results on the homoclinic solutions of difference equations have been obtained.
Erbe, Lynn, Jia, Baoguo, Zhang, Qinqin
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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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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
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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 +2 more
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