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| In this talk we focus on the existence of non-trivial solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions introduced by Servadei and Valdinoci. By using Three Critical Point Theorem and Morse theory, multiplicity results for the above-mentioned equations are obtained. As a particular case, we present some multiplicity results for the fractional Laplacian. Our results extend classical results for semilinear elliptic boundary value problems to the non-local fractional context. |
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