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Abstrakty
The paper deals with the existence of solutions for quasilinear elliptic systems involving singular and convection terms with variable exponents. The approach combines the sub-supersolutions method and Schauder’s fixed point theorem.
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Tom
Strony
105--134
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- Applied Mathematics Laboratory (LMA), Faculty of Exact Sciences and Biology Departement, Faculty of Natural & Life Sciences, A. Mira Bejaia University, Targa Ouzemour, 06000 Bejaia, Algeria
autor
- Departement of Mathematics and Informatic, Faculty of Exact and Natural Sciences, Laboratory LAMIA, University of Antilles, Campus of Fouillole, 97159 Pointe-à-Pitre, Guadeloupe (FWI)
autor
- Departement of Mathematics and Informatic, Faculty of Exact and Natural Sciences, Laboratory LAMIA, University of Antilles, Campus of Fouillole, 97159 Pointe-à-Pitre, Guadeloupe (FWI)
Bibliografia
- [1] C.O. Alves, A. Moussaoui, Existence and regularity solutions for a class of singular (p(x), q(x))-Laplacian systems, Complex Var. Elliptic Equ. 63 (2018), 188–210.
- [2] C.O. Alves, A. Moussaoui, Existence of solutions for a class of singular elliptic systems with convection term, Asymptot. Anal. 90 (2013), 237–248.
- [3] C.O. Alves, A. Moussaoui, L. Tavares, An elliptic system with logarithmic nonlinearity, Adv. Nonlinear Anal. 8 (2019), 928–945.
- [4] D. Banks, An integral inequality, Proc. Amer. Math. Soc. 14 (1963), 823–828.
- [5] H. Brézis, Analyse fonctionnelle. Théorie et applications, Masson, Paris, 1983.
- [6] H. Bueno, G. Ercole, A quasilinear problem with fast growing gradient, Appl. Math. Lett. 26 (2013), 520–523.
- [7] P. Candito, R. Livrea, A. Moussaoui, Singular quasilinear elliptic systems involving gradient terms, Nonlinear Anal. Real World Appl. 55 (2020), 103142.
- [8] A. Cianchi, V. Maz’ya, Global gradient estimates in elliptic problems under minimal data and domain regularity, Commun. Pure Appl. Anal. 14 (2015), 285–311.
- [9] H. Dellouche, A. Moussaoui, Singular quasilinear elliptic systems with gradient dependence, Positivity 26 (2022), Article no. 10.
- [10] L. Diening, P. Hästö, P. Harjulehto, M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Springer Berlin, Heidelberg, 2011.
- [11] L.C. Evans, Partial Differential Equations vol. 19, American Mathematical Soc., Providence, 2010.
- [12] X. Fan, Global C1,α regularity for variable exponent elliptic equations in divergence form, J. Differential Equations 235 (2007), 397–417.
- [13] X. Fan, D. Zhao, On the spaces Lp(x)(Ω) and Wm,p(x)(Ω), J. Math. Anal. Appl. 263 (2001), 424–446.
- [14] X.L. Fan, Q.H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problem, Nonlinear Anal. 52 (2003), 1843–1852.
- [15] U. Guarnatto, S.A. Marano, Infinitely many solutions to singular convective Neumann systems with arbitrarily growing reactions, J. Differential Equations 271 (2021), 849–863.
- [16] U. Guarnotta, S.A. Marano, A. Moussaoui, Singular quasilinear convective elliptic systems in RN, Adv. Nonlinear Anal. 11 (2022), 741–756.
- [17] D.D. Hai, Singular boundary value problems for the p-Laplacian, Nonlinear Anal. 73 (2010), 2876–2881.
- [18] H. Hudzik, On generalized Orlicz–Sobolev spaces, Funct. Approx. Comment. Math. 4 (1976), 37–51.
- [19] Y.H. Kim, L. Wang, C. Zhang, Global bifurcation for a class of degenerate elliptic equations with variable exponents, J. Math. Anal. Appl. 371 (2010), 624–637.
- [20] A.C. Lazer, P.J. Mckenna, On a singular nonlinear elliptic boundary-value problem, Proc. Amer. Math. Soc. 111 (1991), 721–730.
- [21] D. Nabab, J. Vélin, On a nonlinear elliptic system involving the (p(x), q(x))-Laplacian operator with gradient dependence, Complex Var. Elliptic Equ. 67 (2021), 1554–1578.
- [22] K. Perera, E.A. Silva, Existence and multiplicity of positive solutions for singular quasilinear problems, J. Math. Anal. Appl. 323 (2006), 1238–1252.
- [23] J.L. Vázquez, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optim. 12 (1984), 191–202.
- [24] E. Zeidler, Nonlinear Functional Analysis and its Applications. I: Fixed-point Theorems, Springer-Verlag, New York, 1986.
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)
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-d037dcbd-20c2-41c4-abc0-df91d5305619