Fixed point theorems under combined topological and variational conditions

Abstract

The new idea is to replace part of the conditions on the operator involved in the classical fixed point theorems of Schauder, Krasnoselskii, Darbo and Sadovskii, by assumptions upon the associated functional, in case that the fixed point equation has a variational form. Fixed points minimizing the associated functionals are obtained via Ekeland’s variational principle and the Palais–Smale compactness condition guaranteed by the topological properties of the nonlinear operators.

Authors

Angela Budescu
Department of Mathematics, Babes-Bolyai University,  Cluj-Napoca, Romania

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Fixed point; Critical point; Compact nonlinear operator; Condensing operator; Ekeland’s variational principle.

Paper coordinates

A. Budescu, R. Precup, Fixed point theorems under combined topological and variational conditions, Results. Math. 70 (2016) no. 3, 487-497, https://doi.org/10.1007/s00025-016-0589-9

PDF

??

About this paper

Journal

Results in Mathematical

Publisher Name

Springer International Publishing

Print ISSN

422-6383

Online ISSN

1420-9012

google scholar link

Related Posts