A local minimum theorem and critical nonlinearities

被引：6

作者：

Bonanno, G. ^{[1
]}

D'Agui, G. ^{[1
]}

O'Regan, D. ^{[2
]}

机构：

[1] Univ Messina, Dept Engn, I-98166 Messina, Italy

[2] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

来源：

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA | 2016年 / 24卷 / 02期

关键词：

Critical growth; nonlinear differential problem; variational methods; Palais-Smale condition; local minimum; VARIATIONAL PRINCIPLE; ELLIPTIC PROBLEMS; FUNCTIONALS;

D O I：

10.1515/auom-2016-0028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：67 / 86

页数：20

共 14 条

[1] COMBINED EFFECTS OF CONCAVE AND CONVEX NONLINEARITIES IN SOME ELLIPTIC PROBLEMS [J].