
Minimax Theory and its Applications 02 (2017), No. 1, 009025 Copyright Heldermann Verlag 2017 Multiple Solutions for a Class of Schrödinger Equations Involving the Fractional pLaplacian Rossella Bartolo Dip. di Meccanica, Matematica e Management, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy rossella.bartolo@poliba.it Alessio Fiscella Dep. de Matemática, IMECC, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda 651, Campinas SP CEP 13083859, Brazil fiscella@ime.unicamp.br [Abstractpdf] We deal with the multiplicity of weak solutions of the nonlocal elliptic equation $$ (\Delta)^s_p u+V(x)\leftu\right^{p2}u = g(x, u) $$ in $\mathbb{R}^N$, where $(\Delta)^s_p$ is the socalled fractional $p$Laplacian, $V$ is a suitable continuous potential and the nonlinearity $g$ grows as $\leftu\right^{p2}u$ at infinity. Our results extend the classical local counterpart, that is when $s=1$. Keywords: Fractional pLaplacian, integrodifferential operator, variational methods, asymptotically linear problem, resonant problem, pseudogenus. MSC: 49J35, 35S15, 58E05; 47J20, 35R11, 35J10, 46E35 [ Fulltextpdf (181 KB)] for subscribers only. 