Multiplicity of nontrivial solutions for a class of nonlinear Kirchhoff-type equations

摘要

This paper deals with the existence of nontrivial solutions of the following Kirchhoff-type equation: − ( a + b ∫ R N | ∇ u | 2 d x ) Δ u + V ( x ) u = f ( x , u ) $- (a+bint_{mathbb{R}^{N}}|abla u|^{2}, dx )Delta u+V(x)u=f(x,u)$ , in R N $mathbb{R}^{N}$ . Under more relaxed assumptions on V and f, some new criteria on the multiplicity of nontrivial solutions are established by combining Morse theory with local linking and Clark’s theorem.