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

Opuscula Mathematica

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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  • Nikolaos S. Papageorgiou
  • ORCID iD 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
  • ORCID iD 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)
  • ORCID iD 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
  • Communicated by Marek Galewski.
  • Received: 2023-09-28.
  • Accepted: 2023-11-22.
  • Published online: 2024-02-15.
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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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