<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

A local minimum theorem and critical nonlinearities

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"A local minimum theorem and critical nonlinearities"}

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...

A local minimum theorem and critical nonlinearities

Published Online: Sep 21, 2017

Page range: 67 - 86

Received: Apr 20, 2015

Accepted: May 18, 2015

DOI: https://doi.org/10.1515/auom-2016-0028

Keywords
Critical growth, nonlinear differential problem, variational methods, Palais- Smale condition, local minimum

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A local minimum theorem and critical nonlinearities

Published Online: Sep 21, 2017

Page range: 67 - 86

Received: Apr 20, 2015

Accepted: May 18, 2015

DOI: https://doi.org/10.1515/auom-2016-0028

KeywordsCritical growth, nonlinear differential problem, variational methods, Palais- Smale condition, local minimum

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Critical growth, nonlinear differential problem, variational methods, Palais- Smale condition, local minimum