A Brezis–Nirenberg splitting approach for nonlocal fractional equations

In this paper we consider problems modeled by the following nonlocal fractional equation (ProQuest: Formulae and/or non-USASCII text omitted), where s [setmembership] (0, 1) is fixed, [Omega] is an open bounded subset of [dbl-struck R] super(n), n > 2s, with Lipschitz boundary, (- Delta ) super(s...

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Bibliographic Details
Published in:Nonlinear analysis 2015-06, Vol.119, p.341-353
Main Authors: Molica Bisci, Giovanni, Servadei, Raffaella
Format: Article
Language:English
Subjects:
Boundaries
Existence theorems
Mathematical analysis
Mathematical models
Nonlinearity
Operators
Splitting
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Summary:In this paper we consider problems modeled by the following nonlocal fractional equation (ProQuest: Formulae and/or non-USASCII text omitted), where s [setmembership] (0, 1) is fixed, [Omega] is an open bounded subset of [dbl-struck R] super(n), n > 2s, with Lipschitz boundary, (- Delta ) super(s) is the fractional Laplace operator and mu is a real parameter. Under two different types of conditions on the functions a and [functionof], by using a famous critical point theorem in the presence of splitting established by Brezis and Nirenberg, we obtain the existence of at least two nontrivial weak solutions for our problem.
ISSN:0362-546X
DOI:10.1016/j.na.2014.10.025