Fast homoclinic solutions for a class of damped vibration problems with subquadratic potentials

被引：22

作者：

Chen, Peng ^{[1
]}

Tang, X. H. ^{[2
]}

机构：

[1] China Three Gorges Univ, Coll Sci, Yichang 443002, Hubei, Peoples R China

[2] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China

来源：

MATHEMATISCHE NACHRICHTEN | 2013年 / 286卷 / 01期

关键词：

Fast homoclinic solutions; damped vibration problem; variational method; MSC (2010) 34C37; 35A15; 37J45; HAMILTONIAN-SYSTEMS; ORBITS; EXISTENCE;

D O I：

10.1002/mana.201100287

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we deal with the existence and multiplicity of homoclinic solutions of the following damped vibration problems (u) over dot(t) + q(t)(u) over dot(t) - L(t)u(t) + del W(t, u(t)) = 0, where L(t) andW(t, x) are neither autonomous nor periodic in t. Our approach is variational and it is based on the critical point theory. We prove existence and multiplicity results of fast homoclinic solutions under general growth conditions on the potential function. Our theorems appear to be the first such result and our results extend some recent works. (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：4 / 16

页数：13