Existence and multiplicity of solutions for a class of fractional Kirchhoff-type problem

Gaofeng Sun; Kaimin Teng

Vol. 19 No. 1 (2014)

Regular Articles

Existence and multiplicity of solutions for a class of fractional Kirchhoff-type problem

Published 2014-05-03

Gaofeng Sun
Kaimin Teng

Gaofeng Sun
Taiyuan University of Technology

Kaimin Teng
Taiyuan University of Technology

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Abstract

In this paper, we establish the existence and multiplicity of solutions to the following fractional Kirchhoff-type problem
\begin{equation*}
M(\|u\|^2)(-\Delta)^s u=f(x,u(x)), \mbox{ in } \Omega u=0 \mbox{ in } \mathbb{R}^N\backslash\Omega,
\end{equation*}
where $N>2s$ with $s\in(0,1)$, $\Omega$ is an open bounded subset of $\mathbb{R}^N$ with Lipschitz boundary, $M$ and $f$ are two continuous functions, and $(-\Delta)^s$ is a fractional Laplace operator. Our main tools are based on critical point theorems and the truncation technique.

Keywords

Fractional Kirchhoff type problem, integrodifferential operator, truncation technique

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Author Biography

Gaofeng Sun

Deparment of Mathematics

Kaimin Teng

Deparment of Mathematics