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Multiple Solutions for Asymptotically Linear Elliptic Systems

Authors:

Affiliation:

(1) Department of Mathematics, Yunnan Normal University, Kunming, 650092, Yunnan, P.R. China;(2) Institute of Mathematics, AMSS, CAS, Beijing, 100080, P.R. China

Abstract:

This paper is concerned with the following periodic Hamiltonian elliptic system

$left{ {begin{array}{lll} { - Delta u + V(x)u = g(x,v)} & {{text{in}}} & {mathbb{R}^N }, { - Delta u + V(x)v = f(x,v)} & {{text{in}}} & {mathbb{R}^N }, {u(x) to 0,,text{and},,v(x) to 0} & {{text{as}}} & {|x| to infty }, end{array} } right.$

where the potential V is periodic and has a positive bound from below, f(x, t) and g(x, t) are periodic in x, asymptotically linear in t as $$|t| rightarrow infty$$

. By using critical point theory of strongly indefinite functionals, existence of a positive ground state solution as well as infinitely many geometrically distinct solutions for odd f and g are obtained. This work was supported partly by NSFC (10561011 and 10671195), NSFC of Yunnan Proviance, and the Foundation of Education Commission of Yunnan Province, China.

Keywords:

KeywordHeading" >. Hamiltonian elliptic system variational method strongly indefinite functional

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