Electron. J. Diff. Equ., Vol. 2016 (2016), No. 151, pp. 1-12.

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

Vincenzo Ambrosio

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.

Submitted May 10, 2016. Published June 20, 2016.
Math Subject Classifications: 35A15, 35R11, 35J92.
Key Words: Fractional p-Laplacian; sign-changing potential; fountain theorem.

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Vincenzo Ambrosio
Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
Università degli Studi di Napoli Federico II
via Cinthia, 80126 Napoli, Italy
email: vincenzo.ambrosio2@unina.it

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