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Three weak solutions for nonlocal fractional equations. (English) Zbl 1317.35279

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.

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
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