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Remarks on some variants of minimal point theorem and Ekeland variational principle with applications

Meghea Irina, Stamin Cristina Stefania

Demonstratio Mathematica

2022

Vol. 55, nr 1

354--379

This paper presents some variants of minimal point theorem together with corresponding variants of Ekeland variational principle. In the second part of this article, there is a discussion on Ekeland variational principle and minimal point theorem relative to it in uniform spaces. The aim of these series of important results is to highlight relations between them, some improvements and specific applications.

On the Steklov problem involving the p(x)-laplacian with indefinite weight

Ali B. K., Ghanmi A., Kefi K.

Opuscula Mathematica

2017

Vol. 37, no. 6

779--794

Under suitable assumptions, we study the existence of a weak nontrivial solution for the following Steklov problem involving the p(x)-Laplacian [formula] Our approach is based on min-max method and Ekeland's variational principle.