Bounded Solutions to nonlinear problems involving the fractional laplacian depending on parameters

Said El Mimouni, Hichem Hajaiejand Patrick Winkert

Published 2016-03-13Version 1

The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue problems involving the fractional Laplace operator and nonlinearities that have subcritical growth. In the second part, based on a variational principle of Ricceri [16], we study a fractional nonlinear problem with two parameters and prove the existence of multiple solutions.