Ground state solutions for Kirchhoff type equations with asymptotically 4-linear nonlinearity

Abstract

This paper is concerned with the following Kirchhoff type equation: {−(a+b∫Ω|∇v|2)Δv=f(x,v)inΩ,v=0on∂Ω. Assuming that the primitive of f is asymptotically 4-linear as |v|→∞, a homeomorphism between the Nehari manifold and a subset of unit sphere is constructed based on some observations and new techniques. Inspired by recent work of Szulkin and Weth (2010), ground state solutions for the equation above are obtained, as well as infinitely many pairs of nontrivial solutions for case f(x,v) ​is odd with respect to v.