Infinitely many solutions for a class of modified nonlinear fourth-order elliptic equations on RN

摘要

This paper is concerned with the following fourth-order elliptic equations△2u?Δu+V(x)u?κ2Δ(u2)u=f(x,u), in RN,where N≤6, κ≥0. Under some appropriate assumptions on V(x) and f(x,u), we prove the existence of infinitely many negative-energy solutions for the above system via the genus properties in critical point theory. Some recent results from the literature are extended.