Existence of homoclinic orbit for second-order nonlinear difference equation

By using the Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order nonlinear difference equation $\Delta \left[p(t)\Delta u(t-1)\right] +f(t,u(t))=0$ has at least one homoclinic orbit, where $t\in \mathbb{Z},\ u\in \mathbb{R}$.

Bibliographic Details
Main Authors:	Peng Chen, Li Xiao
Format:	Article
Language:	English
Published:	University of Szeged 2010-12-01
Series:	Electronic Journal of Qualitative Theory of Differential Equations
Online Access:	http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=532

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spelling	doaj-faddb1323a704a62863e0023c7172cf02021-07-14T07:21:22ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752010-12-0120107211410.14232/ejqtde.2010.1.72532Existence of homoclinic orbit for second-order nonlinear difference equationPeng Chen0Li Xiao1China Three Gorges University, Yichang, Hubei, P. R. ChinaCentral South University, Changsha, Hunan, P. R. ChinaBy using the Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order nonlinear difference equation $\Delta \left[p(t)\Delta u(t-1)\right] +f(t,u(t))=0$ has at least one homoclinic orbit, where $t\in \mathbb{Z},\ u\in \mathbb{R}$.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=532
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Peng Chen Li Xiao
spellingShingle	Peng Chen Li Xiao Existence of homoclinic orbit for second-order nonlinear difference equation Electronic Journal of Qualitative Theory of Differential Equations
author_facet	Peng Chen Li Xiao
author_sort	Peng Chen
title	Existence of homoclinic orbit for second-order nonlinear difference equation
title_short	Existence of homoclinic orbit for second-order nonlinear difference equation
title_full	Existence of homoclinic orbit for second-order nonlinear difference equation
title_fullStr	Existence of homoclinic orbit for second-order nonlinear difference equation
title_full_unstemmed	Existence of homoclinic orbit for second-order nonlinear difference equation
title_sort	existence of homoclinic orbit for second-order nonlinear difference equation
publisher	University of Szeged
series	Electronic Journal of Qualitative Theory of Differential Equations
issn	1417-3875 1417-3875
publishDate	2010-12-01
description	By using the Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order nonlinear difference equation $\Delta \left[p(t)\Delta u(t-1)\right] +f(t,u(t))=0$ has at least one homoclinic orbit, where $t\in \mathbb{Z},\ u\in \mathbb{R}$.
url	http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=532
work_keys_str_mv	AT pengchen existenceofhomoclinicorbitforsecondordernonlineardifferenceequation AT lixiao existenceofhomoclinicorbitforsecondordernonlineardifferenceequation
_version_	1721303774690017280

Existence of homoclinic orbit for second-order nonlinear difference equation

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