Infinitely many solutions of superlinear elliptic equation. (English) Zbl 1277.35152

Mao, Anmin; Li, Yang

Abstr. Appl. Anal. 2013, Article ID 769620, 6 p. (2013).

Summary: Via the Fountain theorem, we obtain the existence of infinitely many solutions of the following superlinear elliptic boundary value problem: \(-\Delta u = f(x, u)\) in \(\Omega\), \(u = 0\) on \(\partial\Omega\), where \(\Omega \subset \mathbb R^N (N > 2)\) 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.

MSC:

35J25

Boundary value problems for second-order elliptic equations

Keywords:

infinitely many solutions; superlinear elliptic boundary value problem

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