Multiple solutions for asymptotically quadratic and superquadratic elliptic system of Hamiltonian type

Wen Zhang, Jian Zhang and Fukun Zhao

Applied Mathematics and Computation, 2015, vol. 263, issue C, 36-46

Abstract: This paper is concerned with the following nonperiodic Hamiltonian elliptic system {−Δu+V(x)u=Hv(x,u,v)x∈RN,−Δv+V(x)v=Hu(x,u,v)x∈RN,u(x)→0,v(x)→0as|x|→∞,where z=(u,v):RN→R×R,N ≥ 3, and the potential V(x) is nonperiodic and sign-changing. By applying a generalized linking theorem for strongly indefinite functionals, we establish the existence of multiple solutions for asymptotically quadratic nonlinearity as well as the existence of infinitely many solutions for superquadratic nonlinearity.

Keywords: Hamiltonian elliptic system; Generalized linking theorem; Variational methods; Sign-changing potential; Strongly indefinite functionals (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:263:y:2015:i:c:p:36-46

DOI: 10.1016/j.amc.2015.03.108

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