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Existence of at Least One Homoclinic Solution for a Nonlinear Second-Order Difference Equation

International Journal of Nonlinear Sciences and Numerical Simulation, 2019
This paper presents sufficient conditions for the existence of at least one homoclinic solution for a nonlinear second-order difference equation with p-Laplacian. Our technical approach is based on variational methods.
Martin Bohner, Shapour Heidarkhani, Shahin Moradi   +2 more
exaly   +2 more sources

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The Existence of Homoclinic Solutions for Hyperbolic Equations

Journal of Applied Analysis, 1995
Summary: We present a new variational method general enough to treat the problem of the existence of homoclinic solutions for the following semilinear wave equation: \[ x_{tt} (t,y)-x_{yy} (t,y)+ g\bigl(t,y,x(t,y) \bigr)=0 \quad \text{for} \quad ...
Nowakowski, A., Rogowski, A.
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Homoclinic solutions for ordinary p-Laplacian systems

Applied Mathematics and Computation, 2012
The authors study the ordinary \(p\)-Laplacian system \[ \frac{d}{dt}(\left|\dot{u}(t)\right|^{p-2}\dot{u}(t))+\nabla V(t,u(t))=f(t), \] where \(p> 1\), \(t\in\mathbb R\), \(u\in\mathbb R^{n}\) and \(V\in \mathbb C^{1}(\mathbb R\times\mathbb R^{n},\mathbb R)\), \(V(t,x)=-K(t,x)+W(t,x)\) is \(T\)-periodic with respect to \(t\), \(T>0\), and \(f:\mathbb ...
Xiang Lv, Shiping Lu
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Bifurcation of Homoclinic Solutions for Hamiltonian Systems

Zeitschrift für Analysis und ihre Anwendungen, 2002
We consider the Hamiltonian system Ju'(x) + Mu(x) – \bigtriangledown _u F(x,u(x)) = \lambda u(x). Using variational methods obtained by Stuart on the one hand and by Giacomoni and Jeanjean on the other, we get bifurcation results for homoclinic solutions by imposing ...
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Existence of Homoclinic Solutions for a Class of Damped Vibration Problems

Qualitative Theory of Dynamical Systems, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huijuan Xu, Shan Jiang, Guanggang Liu
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Variational Approach to Homoclinic Solutions for Fractional Hamiltonian Systems

Journal of Optimization Theory and Applications, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nemat Nyamoradi, Yong Zhou 0005, Bashir Ahmad 0003, Ahmed Alsaedi   +3 more
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Homoclinic Solutions of Differential Equations

2001
In recent years, starting with works of Bolotin [Bol], Coti-Zelati, Ekeland and Sere [CZES], Coti-Zelati & Rabinowitz [CZR1], [CZR2], Rabinowitz [Ra4], variational methods have been applied to study the existence of homoclinic and heteroclinic solutions of second-order equations and Hamiltonian systems.
Maria do Rosário Grossinho, Stepan Agop Tersian   +1 more
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Homoclinic solutions for Davey-Stewartson equation

Chaos, Solitons & Fractals, 2008
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Huang, Jian, Dai, Zhengde
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The Homoclinic Orbit Solution for Functional Equation

Communications in Theoretical Physics, 2002
In this paper, some examples, such as iterated functional systems, scaling equation of wavelet transform, and invariant measure system, are used to show that the homoclinic orbit solutions exist in the functional equations too. And the solitary wave exists in generalized dynamical systems and functional systems.
Liu Shi-Da, Fu Zun-Tao, Liu Shi-Kuo, Ren Kui   +3 more
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Homoclinic and heteroclinic solutions of upheaval buckling

Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1997
Summary: Upheaval of a heavy flexible strut from a rigid bed is viewed as an initial value problem, and spatial kinetic and potential energy functions are consequently defined. Upheaval from a perfectly flat state is characterized by the simultaneous vanishing of both functions at the boundaries.
Hunt, G. W., Blackmore, A.
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