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Singular quasilinear convective systems involving variable exponents

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
105--134
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
  • 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
Identyfikator YADDA
bwmeta1.element.baztech-d037dcbd-20c2-41c4-abc0-df91d5305619
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