Publication

A local minimum theorem and critical nonlinearities

Bonanno, Gabriele
; 
D’Aguì, Giuseppina
; 
O’Regan, Donal
Identifiers
http://hdl.handle.net/10379/10473
 https://doi.org/10.13025/28799
Publication Date
2016-01-01
Keywords
critical growth, nonlinear differential problem, variational methods, palais-smale condition, local minimum, variational principle, elliptic problems, functionals
Type
Article
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Citation
Bonanno, Gabriele; D’Aguì, Giuseppina; O’Regan, Donal (2016). A local minimum theorem and critical nonlinearities. Analele Universitatii "Ovidius" Constanta - Seria Matematica 24 (2), 67-86
Abstract
In this paper the existence of two positive solutions for a Dirichlet problem having a critical growth, and depending on a real parameter, is established. The approach is based on methods which are totally variational, unlike the fundamental result of Ambrosetti, Brezis and Cerami where a clever combination of topological and variational methods is used in order to obtain the same conclusion. In addition, a numerical estimate of real parameters, for which the two solutions are obtained, is provided. Our main tool is a local minimum theorem.
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Publisher
Walter de Gruyter GmbH
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)