Nontrivial solutions of superlinear nonlocal problems

Giovanni Molica Bisci; Dušan Repovš; Raffaella Servadei

doi:10.1515/forum-2015-0204

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arXiv · 1612.02984

Nontrivial solutions of superlinear nonlocal problems

Giovanni Molica Bisci·Dušan Repovš·Raffaella Servadei

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Abstract

We study the question of the existence of infinitely many weak solutions for nonlocal equations of fractional Laplacian type with homogeneous Dirichlet boundary data, in presence of a superlinear term. Starting from the well-known Ambrosetti-Rabinowitz condition, we consider different growth assumptions on the nonlinearity, all of superlinear type. We obtain three different existence results in this setting by using the Fountain Theorem, which extend some classical results for semilinear Laplacian equations to the nonlocal fractional setting.

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Giovanni Molica Bisci, Dušan Repovš, Raffaella Servadei. 2016-12-09. Nontrivial solutions of superlinear nonlocal problems. https://doi.org/10.1515/forum-2015-0204

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