Anisotropic singular logistic equations

• Autorzy: Silva João Pablo Pinheiro Da , Failla Giuseppe , Gasiński Leszek , Papageorgiou Nikolaos S.

Identyfikatory

DOI

10.7494/OpMath.2025.45.6.765

• Języki publikacji: EN

Abstrakty

EN

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 λ > 0.

Słowa kluczowe

EN

anisotropic (p, q)-Laplacian; superdiffusive perturbation; anisotropic regularity; Hardy’s inequality; strong comparison

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2025
• Tom: Vol. 45, no. 6
• Strony: 765--783
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Silva João Pablo Pinheiro Da

• Universidade Federal do Pará, Departamento de Matemática, 66075-110, Belém, PA, Brazil

• https://orcid.org/0000-0003-3002-8242

autor

Failla Giuseppe

• Department of Mathematics and Computer Sciences, Physical Sciences and Earth Sciences (MIFT), University of Messina, Viale Ferdinando Stagno d’Alcontres, 98166, Messina, Italy

• https://orcid.org/0009-0007-7336-4410

autor

Gasiński Leszek

• University of the National Education Commission, Department of Mathematics, Podchorazych 2, 30-084 Cracow, Poland

• https://orcid.org/0000-0001-8692-6442

autor

Papageorgiou Nikolaos S.

• 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

• https://orcid.org/0000-0003-4800-1187

Bibliografia

• [1] L. Diening, P. Harjulehto, P. Hästö, M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents, Springer, Heidelberg, 2011.
• [2] X.L. Fan, Global C1,α regularity for variable exponent elliptic equations in divergence form, J. Differential Equations 235 (2007), 397–417.
• [3] X.L. Fan, Q.H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problem, Nonlinear Anal. 52 (2003), 1843–1852.
• [4] M.E. Filippakis, N.S. Papageorgiou, Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-Laplacian, J. Differential Equations 245 (2008), 1883–1922.
• [5] S. Hu, N.S. Papageorgiou, Research Topics in Analysis, Vol. II. Applications, Birkhäuser/Springer, Cham, 2024.
• [6] G.M. Lieberman, The natural generalization of the natural conditions of Ladyzhenskaya and Ural’tseva for elliptic equations, Comm. Partial Differential Equations 16 (1991), 311–361.
• [7] N.S. Papageorgiou, P. Winkert, Existence and nonexistence of positive solutions for singular (p, q)-equations with superdiffusive perturbation, Results Math. 76 (2021), Paper no. 169.
• [8] N.S. Papageorgiou, P. Winkert, Positive solutions for singular anisotropic (p, q)-equations, J. Geom. Anal. 31 (2021), 11849–11877.
• [9] N.S. Papageorgiou, P. Winkert, Applied Nonlinear Functional Analysis, De Gruyter, Berlin, 2024.
• [10] N.S. Papageorgiou, V. Rădulescu, X. Tang, Anisotropic Robin problems with logistic reaction, Z. Angew. Math. Phys. 72 (2021), Paper no. 94.
• [11] N.S. Papageorgiou, V. Rădulescu, Y. Zhang, Anisotropic singular double phase Dirichlet problems, Discrete Contin. Dyn. Syst. Ser. S 14 (2021), 4465–4502.
• [12] Q. Zhang, A strong maximum principle for differential equations with nonstandard p(x)-growth conditions, J. Math. Anal. Appl. 312 (2005), 24–32.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)