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Bounded solutions to nonlinear problems in \(\mathbb{R}^N\) involving the fractional Laplacian depending on parameters. (English) Zbl 1444.35147

Summary: 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 \((-\Delta)^s\) and nonlinearities that have subcritical growth. In the second part, based on a variational principle of B. Ricceri [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 9, 4151–4157 (2009; Zbl 1187.47057)], we study a fractional nonlinear problem with two parameters and prove the existence of multiple solutions.

MSC:

35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
35A15 Variational methods applied to PDEs

Citations:

Zbl 1187.47057
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