## Abstract and Applied Analysis

### Three Weak Solutions for Nonlocal Fractional Laplacian Equations

#### Abstract

The existence of three weak solutions for the following nonlocal fractional equation $(-\mathrm{\Delta }{)}^{s}u-\lambda u=\mu f(x,u)$ in $\mathrm{}\mathrm{}\mathrm{\Omega },\mathrm{}u=\mathrm{0}\mathrm{}$ in ${\Bbb R}^{n}\setminus \mathrm{\Omega },$ is investigated, where $s\in (\mathrm{0,1})$ is fixed, $(-\mathrm{\Delta }{)}^{s}$ is the fractional Laplace operator, $\lambda$ and $\mu$ are real parameters, $\mathrm{\Omega }$ is an open bounded subset of ${\Bbb R}^{n}$, $n>\mathrm{2}s$, and the function $f$ satisfies some regularity and natural growth conditions. The approach is based on a three-critical-point theorem for differential functionals.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 809769, 7 pages.

Dates
First available in Project Euclid: 26 March 2014

https://projecteuclid.org/euclid.aaa/1395858529

Digital Object Identifier
doi:10.1155/2014/809769

Mathematical Reviews number (MathSciNet)
MR3166658

Zentralblatt MATH identifier
07023122

#### Citation

Yang, Dandan; Bai, Chuanzhi. Three Weak Solutions for Nonlocal Fractional Laplacian Equations. Abstr. Appl. Anal. 2014 (2014), Article ID 809769, 7 pages. doi:10.1155/2014/809769. https://projecteuclid.org/euclid.aaa/1395858529

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