Localization and multiplicity in the homogenization of nonlinear problems


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.


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

Renata Bunoiu


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

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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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Advances in Nonlinear Analysis


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De Gruyter

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