Opuscula Mathematica
Opuscula Math. 45, no. 6 (2025), 765-783

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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About the authors ▼
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
About the article ▼
Communicated by Marek Galewski.
Received: 2025-06-14.
Accepted: 2025-11-11.
Published online: 2025-12-08.
Cite this article as ▼
João Pablo Pinheiro Da Silva, Giuseppe Failla, Leszek Gasiński, Nikolaos S. Papageorgiou, Anisotropic singular logistic equations, Opuscula Math. 45, no. 6 (2025), 765-783, https://doi.org/10.7494/OpMath.2025.45.6.765.
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