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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.