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## Multiple solutions for a fractional p-Laplacian equation with sign-changing potential

### Abstract

We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the fractional p-Laplace equation $$\displaylines{ (-\Delta)_p^s u + V(x) |u|^{p-2}u = f(x, u) \quad \text{in } \mathbb{R}^N, }$$ where $s\in (0,1)$, $p\geq 2$, $N\geq 2$, $(- \Delta)_{p}^s$ is the fractional p-Laplace operator, the nonlinearity f is p-superlinear at infinity and the potential V(x) is allowed to be sign-changing

Topics: Fractional p-Laplacian, sign-changing potential, fountain theorem, Mathematics, QA1-939
Publisher: Texas State University
Year: 2016
OAI identifier: oai:doaj.org/article:c1810c34be5e48c597ce3b1d5c3ea90d
Journal: