A local minimum theorem and critical nonlinearities-Reference-Cited by-同舟云学术

A local minimum theorem and critical nonlinearities

Published:2016-06-01 Issue:2 Volume:24 Page:67-86
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Bonanno Gabriele¹,D’Aguì Giuseppina¹,O’Regan Donal²

Affiliation:

1. Department of Engineering, University of Messina, c/da Di Dio, Messina 98166 - Italy

2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway , Ireland

Abstract

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.

Publisher

Walter de Gruyter GmbH

Reference14 articles.

1. [1] A. Ambrosetti, H. Brézis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994), 519-543.

2. [2] G. Bonanno, G. Barletta and D. O'Regan, A variational approach to multiplicity results for boundary-value problems on the real line, Proc. Roy. Soc. Edinburgh Sect. A, 145 (2015), 13-29.

3. [3] G. Bonanno, A critical point theorem via the Ekeland variational princi- ple, Nonlinear Anal. 75 (2012), 2992-3007.

4. [4] G. Bonanno, Relations between the mountain pass theorem and local min- ima, Adv. Nonlinear Anal. 1 (2012), 205-220.

5. [5] G. Bonanno and P. Candito, Non-differentiable functionals and applica- tions to elliptic problems with discontinuous nonlinearities, J. Differential Equations 244 (2008), 3031-3059.

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