Existence of nontrivial solutions for modified nonlinear fourth-order elliptic equations with indefinite potential

Abstract

In this paper, we investigate the following modified nonlinear fourth-order elliptic equations{Δ2u−Δu+V(x)u−12uΔ(u2)=g(u),inRN,u∈H2(RN) where Δ2=Δ(Δ) is the biharmonic operator, V is an indefinite potential, g grows subcritically and satisfies the Ambrosetti-Rabinowitz type condition g(t)t≥μG(t)≥0 with μ>3. Using Morse theory, we obtain nontrivial solutions of the above equations. Our result complements recent results in [17], where g has to be 3-superlinear at infinity.