Existence of time homoclinic solutions for a class of discrete wave equationsReport as inadecuate

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Advances in Difference Equations

, 2015:358

First Online: 24 November 2015Received: 15 June 2015Accepted: 11 November 2015


In this paper, a class of nonperiodic discrete wave equations with Dirichlet boundary conditions are obtained by using the center-difference method. It is a strongly indefinite discrete Hamiltonian system. By using a variant and generalized weak linking theorem, the existence of the nontrivial time homoclinic solutions for the system will be obtained. The obtained main results here allow the classical Ambrosetti-Rabinowitz superlinear condition to be replaced by a general superquadratic condition. Such a method cannot be used for the corresponding continuous wave equations, however, it is valid for some general discrete Hamiltonian systems. Similarly, the existence of homoclinic periodic solutions can also be considered.

Keywordsdiscrete wave equation difference system homoclinic solutions linking theorem Ambrosetti-Rabinowitz condition homoclinic periodic solution MSC39A14  Download fulltext PDF

Author: Xinfu Li - Guang Zhang

Source: https://link.springer.com/

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