Abstract
We consider nonlinear elliptic Dirichlet problems with a singular term, a concave (i.e., (p − 1)-sublinear) term and a Carathéodory perturbation. We study the cases where the Carathéodory perturbation is (p − 1)-linear and (p − 1)-superlinear near +∞. Using variational techniques based on the critical point theory together with truncation arguments and the method of upper and lower solutions, we show that if the L ∞-coefficient of the concave term is small enough, the problem has at least two nontrivial smooth solutions.
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The authors wish to thank a knowledgeable referee for bringing to their attention additional important works on the subject.
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Communicated by Rafael D. Benguria.
This research has been partially supported by the Ministry of Science and Higher Education of Poland under Grant no. N201 542438.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Gasiński, L., Papageorgiou, N.S. Nonlinear Elliptic Equations with Singular Terms and Combined Nonlinearities. Ann. Henri Poincaré 13, 481–512 (2012). https://doi.org/10.1007/s00023-011-0129-9
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DOI: https://doi.org/10.1007/s00023-011-0129-9