We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the fractional p-Laplace equation $$ (-\Delta)^{s}_{p}u + V(x) |u|^{p-2}u = f(x, u) in \mathbb{R}^{N}, $$ where $s\in (0, 1)$, $p\geq 2$, $N\geq 2$, $(-\Delta)^{s}_{p}$ 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.

Multiple solutions for a fractional p-Laplacian equation with sign-changing potential / Ambrosio, Vincenzo. - In: ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 1072-6691. - 2016:151(2016), pp. 1-12.

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

Ambrosio, Vincenzo
2016-01-01

Abstract

We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the fractional p-Laplace equation $$ (-\Delta)^{s}_{p}u + V(x) |u|^{p-2}u = f(x, u) in \mathbb{R}^{N}, $$ where $s\in (0, 1)$, $p\geq 2$, $N\geq 2$, $(-\Delta)^{s}_{p}$ 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.
2016
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/264878
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