The aim of this paper is investigating the existence of weak solutions to non--local equations involving a general integro--differential operator of fractional type, when the nonlinearity is subcritical and asymptotically linear at infinity. These equations admit a variational structure and, in presence of an odd symmetric nonlinearity, we prove multiplicity results by using a pseudo--index theory related to the genus. As a particular case we derive existence and multiplicity results for non--local equations involving the fractional Laplacian operator.

A pseudo--index approach to fractional equations / Bartolo, Rossella; Bisci, G. M.. - In: EXPOSITIONES MATHEMATICAE. - ISSN 0723-0869. - 33:4(2015), pp. 502-516. [10.1016/j.exmath.2014.12.001]

A pseudo--index approach to fractional equations

BARTOLO, Rossella;
2015-01-01

Abstract

The aim of this paper is investigating the existence of weak solutions to non--local equations involving a general integro--differential operator of fractional type, when the nonlinearity is subcritical and asymptotically linear at infinity. These equations admit a variational structure and, in presence of an odd symmetric nonlinearity, we prove multiplicity results by using a pseudo--index theory related to the genus. As a particular case we derive existence and multiplicity results for non--local equations involving the fractional Laplacian operator.
2015
A pseudo--index approach to fractional equations / Bartolo, Rossella; Bisci, G. M.. - In: EXPOSITIONES MATHEMATICAE. - ISSN 0723-0869. - 33:4(2015), pp. 502-516. [10.1016/j.exmath.2014.12.001]
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/11589/8119
Citazioni
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 8
social impact