Positive solutions for nonparametric anisotropic singular solutions

• Autorzy: Papageorgiou Nikolaos S. , Rădulescu Vicenţiu D. , Sun Xueying

Identyfikatory

DOI

10.7494/OpMath.2024.44.3.409

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

variable Lebesgue; Sobolev spaces; anisotropic regularity; anisotropic maximum principle; truncations and comparisons; Hardy inequality

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 3
• Strony: 409--423
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Papageorgiou Nikolaos S.

• National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
• University of Craiova, Department of Mathematics, 200585 Craiova, Romania

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

autor

Rădulescu Vicenţiu D.

• 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

• https://orcid.org/0000-0003-4615-5537

autor

Sun Xueying

• Harbin Engineering University, College of Mathematical Sciences, Harbin 150001, People’s Republic of China
• University of Craiova, Department of Mathematics, 200585 Craiova, Romania

• https://orcid.org/0009-0002-7598-9725

Bibliografia

• [1] Y. Bai, N.S. Papageorgiou, S. Zeng, A singular eigenvalue problem for the Dirichlet (p, q)-Laplacian, Math. Z. 300 (2022), 325–345.
• [2] S. Byun, E. Ko, Global C1,α regularity and existence of multiple solutions for singular p(x)-Laplacian equations, Calc. Var. Partial Differential Equations 56 (2017), Article no. 76.
• [3] D.V. Cruz-Uribe, A. Fiorenza, Variable Lebesgue Spaces: Foundations and Harmonic Analysis, Springer Science & Business Media, 2013.
• [4] L. Diening, P. Harjulehto, P. Hästo, M. Ruzička, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Math., vol. 2017, Springer, Heidelberg, 2011.
• [5] X. Fan, Global C1,α regularity for variable exponent elliptic equations in divergence form, J. Differential Equations 235 (2007), no. 2, 397–417.
• [6] X. Fan, D. Zhao, A class of De Giorgi type and Hölder continuity, Nonlinear Anal. 36 (1999), 295–318.
• [7] L. Gasinski, N.S. Papageorgiou, Nonlinear Analysis, Chapman & Hall/CRC, Boca Ratom, Fl, 2006.
• [8] U. Guarnotta, S.A. Marano, A. Moussaoui, Singular quasilinear convective elliptic systems in RN, Adv. Nonlinear Anal. 11 (2022), no. 1, 741–756.
• [9] P. Harjulehto, P. Hästo, M. Koskenoja, Hardy’s inequality in a variable exponent Sobolev space, Georgian Math. J. 12 (2005), 431–442.
• [10] N.S. Papageorgiou, Double phase problems: a survey of some recent results, Opuscula Math. 42 (2022), no. 2, 257–278.
• [11] N.S. Papageorgiou, G. Smyrlis, A bifurcation-type theorem for singular nonlinear elliptic equations, Methods Appl. Anal. 22 (2015), 147–170.
• [12] N.S. Papageorgiou, V.D. Rădulescu, D.D. Repovš, Nonlinear Analysis – Theory and Methods, Springer Monographs in Mathematics, Springer, Cham, 2019.
• [13] N.S. Papageorgiou, V.D. Rădulescu, D.D. Repovš, Anisotropic equations with indefinite potential and competing nonlinearities, Nonlinear Anal. 201 (2020), Article no. 111861.
• [14] N.S. Papageorgiou, V.D. Rădulescu, Y. Zhang, Anisotropic singular double phase Dirichlet problems, Discrete Contin. Dyn. Syst. Ser. S 14 (2021), 4465–4502.
• [15] K. Saoudi, A. Ghanmi, A multiplicity results for a singular equation involving the p(x)-Laplace operator, Complex Var. Elliptic Equ. 62 (2017), no. 5, 695–725.
• [16] P. Takač, J. Giacomoni, A p(x)-Laplacian extension of the Díaz–Saa inequality and some applications, Proc. Roy. Soc. Edinburgh Sect. A 150A (2020), 205–232.
• [17] S. Zeng, N.S. Papageorgiou, Positive solutions for (p, q)-equations with convection and a sign-changing reaction, Adv. Nonlinear Anal. 11 (2022), no. 1, 40–57.
• [18] 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 MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)