El Manouni, Said; Hajaiej, Hichem; Winkert, Patrick Bounded solutions to nonlinear problems in \(\mathbb{R}^N\) involving the fractional Laplacian depending on parameters. (English) Zbl 1444.35147 Minimax Theory Appl. 2, No. 2, 265-283 (2017). 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. Cited in 2 Documents MSC: 35R11 Fractional partial differential equations 26A33 Fractional derivatives and integrals 35A15 Variational methods applied to PDEs Keywords:fractional Laplacian; nonlocal eigenvalue problems; unbounded domains; existence and regularity; multiplicity results; Ricceri’s principle Citations:Zbl 1187.47057 PDFBibTeX XMLCite \textit{S. El Manouni} et al., Minimax Theory Appl. 2, No. 2, 265--283 (2017; Zbl 1444.35147) Full Text: arXiv Link