A Schechter type critical point result in annular conical domains of a Banach space and applications

Abstract

Using Ekeland’s variational principle we obtain a critical point theorem of Schechter type for extrema of a functional in an annular conical domain of a Banach space. The result can be seen as a variational analogue of Krasnoselskii’s fixed point theorem in cones and can be applied for the existence, localization and multiplicity of the positive solutions of variational problems.The result is then applied to p-Laplace equations, where the geometric condition on the boundary of the annular conical domain is established via a weak Harnack type inequality given in terms of the energetic norm. This method can be applied also to other homogeneous operators in order to obtain existence, multiplicity or infinitely many solutions for certain classes of quasilinear equations.

Authors

Hannelore Lisei
Babes-Bolyai University, Cluj-Napoca, Romania

Radu Precup
Babes-Bolyai University, Cluj-Napoca, Romania

Csaba Varga
Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

weak Harnack inequality; Ekeland’s variational principle; p-Laplacian; Critical point; extremum point; Palais-Smale condition.

Paper coordinates

H. Lisei, R. Precup, C. Varga, A Schechter type critical point result in annular conical domains of a Banach space and applications, Discrete Contin. Dyn. Syst. 36 (2016), 3775-3789, http://dx.doi.org/10.3934/dcds.2016.36.3775

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About this paper

Journal

Discrete Continuous Dynamical

Publisher Name

American Institute of Mathematical Sciences

 

Print ISSN

1937-1632

Online ISSN

1937-1179

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