Molica Bisci, Giovanni; Pansera, Bruno Antonio Three weak solutions for nonlocal fractional equations. (English) Zbl 1317.35279 Adv. Nonlinear Stud. 14, No. 3, 619-629 (2014). From the abstract: This article concerns a class of nonlocal fractional Laplacian problems depending of three real parameters. More precisely, by using an appropriate analytical context on fractional Sobolev spaces due to Servadei and Valdinoci (in order to correctly encode the Dirichlet boundary datum in the variational formulation of our problem) we establish the existence of three weak solutions for fractional equations via a recent abstract critical point result for differentiable and parametric functionals recently proved by Ricceri. Reviewer: Junichi Aramaki (Saitama) Cited in 20 Documents MSC: 35R11 Fractional partial differential equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35D30 Weak solutions to PDEs 35B38 Critical points of functionals in context of PDEs (e.g., energy functionals) 35J20 Variational methods for second-order elliptic equations 35J62 Quasilinear elliptic equations 35J92 Quasilinear elliptic equations with \(p\)-Laplacian Keywords:fractional Laplacian; fractional Sobolev space; variational formulation; critical points PDFBibTeX XMLCite \textit{G. Molica Bisci} and \textit{B. A. Pansera}, Adv. Nonlinear Stud. 14, No. 3, 619--629 (2014; Zbl 1317.35279)