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Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media

Abstract

We study nonlinear eigenvalue problems of the type in, where is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality. A specific minimax method is developed without making use of Palais-Smale condition.

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Correspondence to Dumitru Motreanu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Motreanu, D., RăDulescu, V. Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media. Bound Value Probl 2005, 708605 (2005). https://doi.org/10.1155/BVP.2005.107

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  • DOI: https://doi.org/10.1155/BVP.2005.107