Opuscula Math. 45, no. 6 (2025), 765-783
https://doi.org/10.7494/OpMath.2025.45.6.765
Opuscula Mathematica
Anisotropic singular logistic equations
João Pablo Pinheiro Da Silva
Giuseppe Failla
Leszek Gasiński
Nikolaos S. Papageorgiou
Abstract. We consider a parametric Dirichlet problem driven by the anisotropic \((p,q)\)-Laplacian and a reaction with a singular term and a superdiffusive logistic perturbation. We prove an existence and nonexistence theorem which is global with respect to the parameter \(\lambda\gt 0\).
Keywords: anisotropic \((p,q)\)-Laplacian, superdiffusive perturbation, anisotropic regularity, Hardy's inequality, strong comparison.
Mathematics Subject Classification: 35J60, 35J75.
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- João Pablo Pinheiro Da Silva (corresponding author)
https://orcid.org/0000-0003-3002-8242- Universidade Federal do Pará, Departamento de Matemática, 66075-110, Belém, PA, Brazil
- Giuseppe Failla
- https://orcid.org/0009-0007-7336-4410
- Department of Mathematics and Computer Sciences, Physical Sciences and Earth Sciences (MIFT), University of Messina, Viale Ferdinando Stagno d'Alcontres, 98166, Messina, Italy
- Leszek Gasiński
- https://orcid.org/0000-0001-8692-6442
- University of the National Education Commission, Department of Mathematics, Podchorazych 2, 30-084 Cracow, Poland
- Nikolaos S. Papageorgiou
- https://orcid.org/0000-0003-4800-1187
- National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
- Center for Applied Mathematics, Yulin Normal University, Yulin 537000, P.R. China
- University of Craiova, Department of Mathematics, 200585 Craiova, Romania
- Communicated by Marek Galewski.
- Received: 2025-06-14.
- Accepted: 2025-11-11.
- Published online: 2025-12-08.
