Bounded Solutions to Nonlinear Problems in R Involving the Fractional Laplacian Depending on Parameters
Keywords:
Fractional Laplacian, nonlocal eigenvalue problems, unbounded domains, existence and regularity, multiplicity results, Ricceri’s principle.Abstract
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 ∆s and nonlinearities that have subcritical growth. In the second part, based on a variational principle of Ricceri [17], we study a fractional nonlinear problem with two parameters and prove the existence of multiple solutions.
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