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Some existence results for a nonlocal non-isotropic problem

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EN
Abstrakty
EN
In this paper we deal with the following problem [formula] where Ω is a bounded regular domain in RN . We will assume without loss of generality that [formula] PN and that ƒ and g are non-negative functions belonging to a suitable Lebesgue space [formula].
Rocznik
Strony
5--23
Opis fizyczny
Bibliogr. 34 poz.
Twórcy
  • Universite de Tlemcen Depatement GEE Laboratoire d’Analyse Non Lineaire et Mathematiques Appliquees BP 119 Tlemcen, 13000, Algeria
  • Universite de Tlemcen Depatement GEE Laboratoire d’Analyse Non Lineaire et Mathematiques Appliquees BP 119 Tlemcen, 13000, Algeria
Bibliografia
  • [1] B. Abdellaoui, A. Attar, S.E. Miri, Nonlinear singular el liptic problem with gradient term and general datum, J. Math. Anal. Appl. 409 (2014), 362-377.
  • [2] K.B. Ali, M. Bezzarga, A. Ghanmi, K. Kefi, Existence of positive solution for Kirchhoff problems, Complex Anal. Oper. Theory. 13 (2019), 115-126.
  • [3] A. Alsaedi, B. Ahmad, Anisotropic problems with unbalanced growth, Adv. Nonlinear Anal. 9 (2020), 1504-1515.
  • [4] C.O. Alves, A. El Hamidi, Existence of solution for a anisotropic equation with critical exponent, Differ. Integral Equ. 21 (2008), 25-40.
  • [5] A. Bensedik, On existence results for an anisotropic el liptic equation of Kirchhoff-type by a monotonicity method, Funkc. Ekvacioj. 57 (2014), 489-502.
  • [6] L. Boccardo, L. Orsina, Semilinear el liptic equations with singular nonlinearities, Calc. Var. Partial Differential Equations 37 (2009), 363-380.
  • [7] Y.O. Boukarabila, S.E. Miri, Anisotropic system with singular and regular nonlinearities, Complex Var. Elliptic Equ. 65 (2020), 621-631.
  • [8] B. Brandolini, F.C. Cirstea, Singular anisotropic elliptic equations with gradient-dependent lower order terms, arXiv:2001.02887 (2020).
  • [9] L.M. De Cave, Nonlinear el liptic equations with singular nonlinearities, Asymptot. Anal. 84 (2013), 181-195.
  • [10] A. Di Castro, El liptic problems for some anisotropic operators, Ph.D. Thesis, University of Rome “Sapienza”, a. y. 2008/2009.
  • [11] A. Di Castro, Existence and regularity results for anisotropic el liptic problems, Adv. Nonlin. Stud. 9 (2009), 367-393.
  • [12] A. Di Castro, Anisotropic el liptic problems with natural growth terms, Manuscripta Math. 135 (2011), 521-543.
  • [13] G.C.G. Dos Santos, G.M. Figueiredo, L.S. Tavares, Existence results for some anisotropic singular problems via sub-supersolutions, Milan J. Math. 87 (2019), 249-272.
  • [14] G.C.G. Dos Santos, L.S. Tavares, Existence results for an anisotropic nonlocal problem involving critical and discontinuous nonlinearities, Complex Var. Elliptic Equ. (2020), 1-25.
  • [15] G.M. Figueiredo, J.R.S. Junior, A. Suarez, Multiplicity results for an anisotropic equation with subcritical or critical growth, Adv. Nonlinear Stud. 15 (2015), 377-394.
  • [16] A. Fiscella, A fractional Kirchhoff problem involving a singular term and a critical nonlinearity, Adv. Nonlinear Anal. 8 (2019), 645-660.
  • [17] I. Fragala, F. Gazzola, B. Kawohl, Existence and nonexistence results for anisotropic quasilinear elliptic equations, Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004), 715-734.
  • [18] M. Ghergu, V. Radulescu, Singular Elliptic Problems, Oxford Univ. Press, 2008.
  • [19] S.N. Kruzhkov, I.M. Kolodii, On the theory of embedding of anisotropic Sobolev spaces, Russian Math. Surveys 38 (1983), 188-189.
  • [20] A.R. Leggat, S.E. Miri, Anisotropic problem with singular nonlinearity, Complex Var. Elliptic Equ. 61 (2016), 496-509.
  • [21] A.R. Leggat, S.E. Miri, Existence and multiplicity results for a doubly anisotropic problem with sign-changing nonlinearity, Note di Mat. 39 (2019), 1-12.
  • [22] C.Y. Lei, J.F. Liao, Multiple positive solutions for Kirchhoff type problems with singularity and asymptotical ly linear nonlinearities, Appl. Math. Lett. 94 (2019), 279-285.
  • [23] Q. Li, W. Gao, Y. Han, Existence of solution for a singular el liptic equation of Kirchhoff type, Mediterr. J. Math. 14 (2017), Article no. 231.
  • [24] J.F. Liao, X.F. Ke, C.Y. Lei, C.L. Tang, A uniqueness result for Kirchhoff type problems with singularity, Appl. Math. Lett. 59 (2016), 24-30.
  • [25] S.E. Miri, Quasilinear el liptic problems with general growth and nonlinear term having singular behavior, Adv. Nonlinear Stud. 12 (2012), 19-48.
  • [26] S.E. Miri, Problemes el liptiques et paraboliques avec terme singulier, Tlemcen University, Doctoral Dissertation, 2015.
  • [27] S.E. Miri, On an anisotropic problem with singular nonlinearity having variable exponent, Ric. di Mat. 66 (2017), 415-424.
  • [28] S.M. Nikolskii, Imbedding theorems for functions with partial derivatives considered in various metrics, Izd. Akad. Nauk SSSR 22 (1958), 321-336.
  • [29] N.S. Papageorgiou, V.D. Radulescu, D.D. Repovs, Nonlinear nonhomogeneous singular problems, Calc. Var. Partial Differential Equations 59 (2020), Article no. 59.
  • [30] V.D. Radulescu, Isotropic and anisotropic double-phase problems: old and new, Opuscula Math. 39 (2019), 259-279.
  • [31] S.H. Rasouli, M. Fani, An existence result for p-Kirchhoff-type problems with singular nonlinearity, Appl. Math. E-Notes 18 (2018), 62-68.
  • [32] M. Troisi, Teoremi di inclusione per spazi di Sobolev non isotropi, Ricerche Mat. 18 (1969), 3-24.
  • [33] D. Wang, B. Yan, A uniqueness result for some Kirchhoff-type equations with negative exponents, Appl. Math. Lett. 92 (2019), 93-98.
  • [34] Q. Zhang, V.D. Radulescu, V.D. Radulescu, Double phase anisotropic variational problems and combined effects of reaction and absorption terms, J. Math. Pures Appl. 118 (2018), 159-203.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-67d79403-dccf-4808-af45-f21bdf14a371
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