Ground state solutions of Nehari‐Pankov type for a superlinear elliptic system on

Abstract

This paper is concerned with the following Schrödinger elliptic system −normalΔu+V(x)u=g(x,v),1emx∈double-struckRN,−normalΔv+V(x)v=f(x,u),1emx∈double-struckRN,u(x)→01emand1emv(x)→0,1em1em1em1emas1em|x|→∞, where the potential V is periodic and 0 lies in a gap of the spectrum of −Δ+V, f(x,t) and g(x,t) are superlinear in t at infinity. By using non‐Nehari manifold method developed recently by Tang, we demonstrate the existence of the ground state solutions of Nehari‐Pankov type for the above problem with periodic and asymptotically periodic nonlinearity. Copyright © 2016 John Wiley & Sons, Ltd.

Existence and multiplicity of solutions for ‐Laplacian equations in

“…For , we refer the reader to with their references. For , we refer the reader to and the references therein. The ‐Laplacian is a generalization of the p ‐Laplacian, and it possesses more complicated nonlinearities than the p ‐Laplacian, due to the fact that the operator is not homogeneous.…”

Time‐harmonic and asymptotically linear Maxwell equations in anisotropic media

“…Condition (F3) together with | f ( x , u )|= o (| u |) as | u |→0 imply that which is a weaker version of the classic Ambrosetti‐Rabinowitz condition. As pointed out in Qin and Tang, condition was first introduced by Schechter (2.7) or (3.1) for scalar Schrödinger equation, and it was commonly used (see Qin and Tang and Tang) instead of the usual monotonic condition:…”