Localization and multiplicity in the homogenization of nonlinear problems

Advances in Nonlinear Analysis

article

Renata Bunoiu¹  Radu Precup² 

[1] University of Lorraine;Faculty of Mathematics and Computer Science, Babeş-Bolyai University

关键词: Nonlinear elliptic problem;    homogenization;    localization;    positive solution;    multiple solutions;   

DOI  :  10.1515/anona-2020-0001

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY