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: $-\mathrm{\Delta }u=f(x,u)$ in $\mathrm{\Omega ,}$$u=0$ on $\partial \Omega$, where $\Omega \subset {ℝ}^N\hspace{0.17em}\hspace{0.17em}(N>2)$ 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.