Infinitely Many Solutions of Superlinear Elliptic Equation

Abstract

Via the Fountain theorem, we obtain the existence of infinitely many solutions of the following superlinear elliptic boundary value problem: −Δu=f(x,u) in Ω,u=0 on ∂Ω, where Ω⊂ℝN (N>2) is a bounded domain with smooth boundary and f is odd in u and continuous. There is no assumption near zero on the behavior of the nonlinearity f, and f does not satisfy the Ambrosetti-Rabinowitz type technical condition near infinity.