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Existence of weak solutions for non-local fractional problems via Morse theory

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  • In this paper, we study the existence of non-trivial solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions. Non-trivial solutions are obtained by computing the critical groups and Morse theory. Our results extend some classical theorems for semilinear elliptic equations to the non-local fractional setting.
    Mathematics Subject Classification: 35J60, 35J91, 58E05.


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