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Minimax Theory and its Applications 02 (2017), No. 1, 009--025
Copyright Heldermann Verlag 2017

Multiple Solutions for a Class of Schrödinger Equations Involving the Fractional p-Laplacian

Rossella Bartolo
Dip. di Meccanica, Matematica e Management, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy

Alessio Fiscella
Dep. de Matemática, IMECC, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda 651, Campinas SP CEP 13083--859, Brazil


We deal with the multiplicity of weak solutions of the non-local elliptic equation $$ (-\Delta)^s_p u+V(x)\left|u\right|^{p-2}u = g(x, u) $$ 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 $\left|u\right|^{p-2}u$ at infinity. Our results extend the classical local counterpart, that is when $s=1$.

Keywords: Fractional p-Laplacian, integro-differential operator, variational methods, asymptotically linear problem, resonant problem, pseudo-genus.

MSC: 49J35, 35S15, 58E05; 47J20, 35R11, 35J10, 46E35

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