A local minimum theorem and critical nonlinearities

Gabriele Bonanno; Giuseppina D’Aguì; Donal O’Regan

doi:10.13025/28799

A local minimum theorem and critical nonlinearities

Gabriele Bonanno
, Giuseppina D’Aguì
, Donal O’Regan

Mathematics

Dipartimento DIMED

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

6 Citations (Scopus)

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.

Original language	English
Pages (from-to)	67-86
Number of pages	20
Journal	Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
Volume	24
Issue number	2
DOIs	https://doi.org/10.13025/28799 https://doi.org/10.1515/auom-2016-0028
Publication status	Published - 2016

Keywords

Critical growth
Local minimum
Nonlinear differential problem
Palais-smale condition
Variational methods

Access to Document

10.13025/28799Licence: CC BY-NC-ND
10.1515/auom-2016-0028

Cite this

@article{7fe091bb674947829031dd05dcf451a7,

title = "A local minimum theorem and critical nonlinearities",

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.",

keywords = "Critical growth, Local minimum, Nonlinear differential problem, Palais-smale condition, Variational methods",

author = "Gabriele Bonanno and Giuseppina D{\textquoteright}Agu{\`i} and Donal O{\textquoteright}Regan",

year = "2016",

doi = "10.13025/28799",

language = "English",

volume = "24",

pages = "67--86",

journal = "Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica",

issn = "1224-1784",

publisher = "Paradigm Publishing Services",

number = "2",

}

TY - JOUR

T1 - A local minimum theorem and critical nonlinearities

AU - Bonanno, Gabriele

AU - D’Aguì, Giuseppina

AU - O’Regan, Donal

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Critical growth

KW - Local minimum

KW - Nonlinear differential problem

KW - Palais-smale condition

KW - Variational methods

UR - http://hdl.handle.net/10379/10473

UR - https://www.scopus.com/pages/publications/84991721738

U2 - 10.13025/28799

DO - 10.13025/28799

M3 - Article

SN - 1224-1784

VL - 24

SP - 67

EP - 86

JO - Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica

JF - Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica

IS - 2

ER -

A local minimum theorem and critical nonlinearities

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this