In this paper we consider a resonance problem driven by a non-local integrodifferential operator L-K with homogeneous Dirichlet boundary conditions. This problem has a variational structure and we find a solution for it using the Saddle Point Theorem. We prove this result for a general integrodifferential operator of fractional type and from this, as a particular case, we derive an existence theorem for a fractional Laplacian equation. This existence theorem extends to the non-local setting some results, already known in the literature in the case of the Laplace operator

A resonance problem for non-local elliptic operators

SERVADEI, RAFFAELLA;
2013

Abstract

In this paper we consider a resonance problem driven by a non-local integrodifferential operator L-K with homogeneous Dirichlet boundary conditions. This problem has a variational structure and we find a solution for it using the Saddle Point Theorem. We prove this result for a general integrodifferential operator of fractional type and from this, as a particular case, we derive an existence theorem for a fractional Laplacian equation. This existence theorem extends to the non-local setting some results, already known in the literature in the case of the Laplace operator
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11576/2626805
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 36
  • ???jsp.display-item.citation.isi??? 34
social impact