The paper deals with equations driven by a non-local integrodifferential operator Lk with homogeneous Dirichlet boundary conditions. These equations have a variational structure and we find a solution for them using the Saddle Point Theorem. We prove this result for a general integrodifferential operator of fractional type and from this, as a particular case, one can derive an existence theorem for the fractional Laplacian, finding solutions of the equation (Formula Presented) where the nonlinear term f satisfies a linear growth condition.

Fiscella, A. (2015). Saddle point solutions for non-local elliptic operators. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 44(2), 527-538 [10.12775/tmna.2014.059].

Saddle point solutions for non-local elliptic operators

Fiscella A
2015

Abstract

The paper deals with equations driven by a non-local integrodifferential operator Lk with homogeneous Dirichlet boundary conditions. These equations have a variational structure and we find a solution for them using the Saddle Point Theorem. We prove this result for a general integrodifferential operator of fractional type and from this, as a particular case, one can derive an existence theorem for the fractional Laplacian, finding solutions of the equation (Formula Presented) where the nonlinear term f satisfies a linear growth condition.
Articolo in rivista - Articolo scientifico
Integrodifferential operators, fractional Laplacian, variational techniques, Saddle Point Theorem, Palais{Smale condition
English
527
538
12
Green Open Access
Fiscella, A. (2015). Saddle point solutions for non-local elliptic operators. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 44(2), 527-538 [10.12775/tmna.2014.059].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/338091
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