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
google scholar link
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