Opuscula Mathematica
Opuscula Math. 44, no. 3 (2024), 409-423

Positive solutions for nonparametric anisotropic singular solutions

Nikolaos S. Papageorgiou
Vicenţiu D. Rădulescu
Xueying Sun
Abstract. We consider an elliptic equation driven by a nonlinear, nonhomogeneous differential operator with nonstandard growth. The reaction has the combined effects of a singular term and of a "superlinear" perturbation. There is no parameter in the problem. Using variational tools and truncation and comparison techniques, we show the existence of at least two positive smooth solutions.
Keywords: variable Lebesgue and Sobolev spaces, anisotropic regularity, anisotropic maximum principle, truncations and comparisons, Hardy inequality.
Mathematics Subject Classification: 35B51, 35J60, 35B65, 35J75, 35J92, 46E35, 47J20, 58E05.
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About the authors ▼
Nikolaos S. Papageorgiou
https://orcid.org/0000-0003-4800-1187
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece; University of Craiova, Department of Mathematics, 200585 Craiova, Romania
Vicenţiu D. Rădulescu
https://orcid.org/0000-0003-4615-5537
AGH University of Krakow, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Kraków, Poland; University of Craiova, Department of Mathematics, 200585 Craiova, Romania
Xueying Sun (corresponding author)
https://orcid.org/0009-0002-7598-9725
Harbin Engineering University, College of Mathematical Sciences, Harbin 150001, People's Republic of China; University of Craiova, Department of Mathematics, 200585 Craiova, Romania
About the article ▼
Communicated by Marek Galewski.
Received: 2023-09-28.
Accepted: 2023-11-22.
Published online: 2024-02-15.
Cite this article as ▼
Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Xueying Sun, Positive solutions for nonparametric anisotropic singular solutions, Opuscula Math. 44, no. 3 (2024), 409-423, https://doi.org/10.7494/OpMath.2024.44.3.409.
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