## Abstract and Applied Analysis

### 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: $-\mathrm{\Delta }u=f\left(x,u\right)$ in $\mathrm{Ω,}$$u=0$ on $\partial Ω$, where $Ω\subset {ℝ}^{N} \left(N>2\right)$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 769620, 6 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511896

Digital Object Identifier
doi:10.1155/2013/769620

Mathematical Reviews number (MathSciNet)
MR3055962

Zentralblatt MATH identifier
1277.35152

#### Citation

Mao, Anmin; Li, Yang. Infinitely Many Solutions of Superlinear Elliptic Equation. Abstr. Appl. Anal. 2013 (2013), Article ID 769620, 6 pages. doi:10.1155/2013/769620. https://projecteuclid.org/euclid.aaa/1393511896

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