The purpose of this paper is to study the existence of solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions. These equations have a variational structure and we find a non-trivial solution for them using the Mountain Pass Theorem. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. We prove this result for a general integrodifferential operator of fractional type and, as a particular case, we derive an existence theorem for the fractional Laplacian. As far as we know, all these results are new.
Mountain Pass solutions for non-local elliptic operators
SERVADEI, RAFFAELLA;
2012
Abstract
The purpose of this paper is to study the existence of solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions. These equations have a variational structure and we find a non-trivial solution for them using the Mountain Pass Theorem. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. We prove this result for a general integrodifferential operator of fractional type and, as a particular case, we derive an existence theorem for the fractional Laplacian. As far as we know, all these results are new.File in questo prodotto:
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