Electron. J. Differential Equations, Vol. 2017 (2017), No. 09, pp. 1-8.

Multiple positive solutions for nonlocal problems involving a sign-changing potential

Chun-Yu Lei, Jia-Feng Liao, Hong-Min Suo

Abstract:
In this article we show the existence and multiplicity of positive solutions for the nonlocal problem with a sign-changing weight function,
$$\displaylines{ -(a-b\int_{\Omega}|\nabla u|^2dx)\Delta u= f_\lambda(x)|u|^{q-2}u, \quad\text{in }\Omega, \cr u=0, \quad\text{on }\partial\Omega, }$$
where $\Omega$ is a smooth bounded domain in $\mathbb{R}^{3}$, $a, b>0,; 1<q<2$. Our technical approach is based on the variational method.

Submitted October 28, 2016. Published January 10, 2017.
Math Subject Classifications: 35J20, 35J30, 35J66.
Key Words: Nonlocal problem; variational method; sign-changing potential; positive solution.

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Chun-Yu Lei
School of Sciences
Gui Zhou Minzu University
Guiyang 550025, China
email: leichygzu@sina.cn
Jia-Feng Liao
School of Mathematics and Information
China West Normal University
Nanchong 637002, China
email: liaojiafeng@163.com
Hong-Min Suo
School of Sciences
Gui Zhou Minzu University
Guiyang 550025, China
email: 11394861@qq.com

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