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abstract: |
    The aim of this paper is to prove multiplicity of solutions for nonlocal fractional equations modeled by $$\left\{
    \begin{array}{ll}
    (-\Delta)^s u-\lambda u=f(x,u) & {\mbox{ in }} \Omega\\
    u=0 & {\mbox{ in }} {\mathbb R}^n\setminus \Omega\,,
    \end{array} \right.$$ where $s\in (0,1)$ is fixed, $(-\Delta)^s$ is the fractional Laplace operator, $\lambda$ is a real parameter, $\Omega\subset {\mathbb R}^n$, $n>2s$, is an open bounded set with continuous boundary and nonlinearity $f$ satisfies natural superlinear and subcritical growth assumptions. Precisely, along the paper we prove the existence of at least three non-trivial solutions for this problem in a suitable left neighborhood of any eigenvalue of $(-\Delta)^s$. At this purpose we employ a variational theorem of mixed type (one of the so-called $\nabla$-theorems).
address:
- 'Dipartimento PAU, Università ‘Mediterranea’ di Reggio Calabria, Via Melissari 24, 89124 Reggio Calabria, Italy'
- 'Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli, 1 06123 Perugia, Italy'
- 'Dipartimento di Scienze di Base e Fondamenti (DiSBeF), Università degli Studi di Urbino ‘Carlo Bo’, Piazza della Repubblica, 13 61029 Urbino (Pesaro e Urbino) ITALY '
author:
- Giovanni Molica Bisci
- Dimitri Mugnai
- Raffaella Servadei
title: 'On multiple solutions for nonlocal fractional problems 