We deal with the multiplicity of weak solutions of the non-local elliptic equation $$ (-Delta)^s_p u+V(x)left|u ight|^{p-2}u = g(x, u) $$ in $mathbb{R}^N$, where $(-Delta)^s_p$ is the so-called fractional $p$-Laplacian, $V$ is a suitable continuous potential and the nonlinearity $g$ grows as $left|u ight|^{p-2}u$ at infinity. Our results extend the classical local counterpart, that is when $s=1$.
Multiple solutions for a class of Schroedinger equations involving the fractional p–Laplacian / Bartolo, Rossella; Fiscella, Alessio. - In: MINIMAX THEORY AND ITS APPLICATIONS. - ISSN 2199-1413. - STAMPA. - 2:1(2017), pp. 9-25.
Multiple solutions for a class of Schroedinger equations involving the fractional p–Laplacian
Bartolo, Rossella;
2017-01-01
Abstract
We deal with the multiplicity of weak solutions of the non-local elliptic equation $$ (-Delta)^s_p u+V(x)left|u ight|^{p-2}u = g(x, u) $$ in $mathbb{R}^N$, where $(-Delta)^s_p$ is the so-called fractional $p$-Laplacian, $V$ is a suitable continuous potential and the nonlinearity $g$ grows as $left|u ight|^{p-2}u$ at infinity. Our results extend the classical local counterpart, that is when $s=1$.File in questo prodotto:
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