Localization and multiplicity in the homogenization of nonlinear problems

Abstract

We propose a method for the localization of solutions for a class of nonlinear problems arising in the homogenization theory. The method combines concepts and results from the linear theory of PDEs, linear periodic homogenization theory, and nonlinear functional analysis. Particularly, we use the Moser-Harnack inequality, arguments of fixed point theory and Ekeland’s variational principle. A significant gain in the homogenization theory of nonlinear problems is that our method makes possible the emergence of finitely or infinitely many solutions.

Authors

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

Renata Bunoiu

Keywords

Nonlinear elliptic problem; homogenization; localization; positive solution; multiple solutions

Paper coordinates

R. Bunoiu, R. Precup, Localization and multiplicity in the homogenization of nonlinear problems, Adv. Nonlinear Anal. 9 (2020), no. 1, 292-304, https://doi.org/10.1515/anona-2020-0001

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About this paper

Journal

Advances in Nonlinear Analysis

 

Publisher Name

De Gruyter

Print ISSN
Online ISSN

2191-950X

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