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

Gaofeng Sun, Kaimin Teng


In this paper, we establish the existence and multiplicity of solutions to the following fractional Kirchhoff-type problem
M(\|u\|^2)(-\Delta)^s u=f(x,u(x)), \mbox{ in } \Omega  u=0 \mbox{ in } \mathbb{R}^N\backslash\Omega,
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.


Fractional Kirchhoff type problem; integrodifferential operator; truncation technique

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ISSN: 1331-0623 (Print), 1848-8013 (Online)