Existence result for a nonlinear elliptic problem by topological degree in Sobolev spaces with variable exponent

[1] M. Ait Hammou and E. Azroul, Construction of a topological degree theory in Generalized Sobolev Spaces, J. of Univ. math., 1 no. 2 (2018), 116–129.10.1007/978-3-030-02155-9_1Search in Google Scholar

[2] M. Ait Hammou, E. Azroul and B. Lahmi, Existence of solutions for p(x)-Laplacian Dirichlet problem by Topological degree, Bull. Transilv. Univ. Bras¸ov Ser. III, 11(60) no. 2 (2018), 29–38.Search in Google Scholar

[3] M. Ait Hammou, E. Azroul and B. Lahmi, Topological degree methods for a Strongly nonlinear p(x)-elliptic problem, Rev. Colombiana Mat., 53 no. 1 (2019), 27–39.10.15446/recolma.v53n1.81036Search in Google Scholar

[4] M. Ait Hammou and E. Azroul, Nonlinear Elliptic Problems in Weighted Variable Exponent Sobolev Spaces by Topological Degree, Proyecciones, 38 no. 4 (2019), 733–751.10.22199/issn.0717-6279-2019-04-0048Search in Google Scholar

[5] M. Ait Hammou and E. Azroul, Nonlinear elliptic boundary value problems by Topological degree, Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications, Studies in Systems, Decision and Control 243, Springer Nature Switzerland AG 2020, doi.org /10.1007/978-3-030-26149-8 1, 1–13.10.1007/978-3-030-26149-8_1Search in Google Scholar

[6] M.L. Ahmed Oubeid, A. Benkirane, M. Sidi El Vally, Nonlinear elliptic equations involving measure data in Museilak-Orlicz-Sobolev spaces, J. of Abstract Diff. Equ. and App., 4 no. 1 (2013), 43–57.Search in Google Scholar

[7] E. Azroul, H. Redwane and C. Yazough, Strongly nonlinear non homogeneous elliptic unilateral problems with L¹ data and no sign conditions, Electron. J. Differential Equations, 2012 no. 79 (2012), 1–20.Search in Google Scholar

[8] S. Antontsev and S. Shmarev, Anisotropic parabolic equations with variable nonlinearity, Publ. Mat., 53 no. 2 (2009), 355–399.10.5565/PUBLMAT_53209_04Search in Google Scholar

[9] J. Berkovits, Extension of the Leray-Schauder degree for abstract Hammerstein type mappings, J. Differ. Equ., 234 (2007), 289–310.10.1016/j.jde.2006.11.012Search in Google Scholar

[10] L.Boccardo and T.Gallouet, Nonlinear elliptic equations involving measure as data, J. Funct. Anal., 87 (1989), 149–169.10.1016/0022-1236(89)90005-0Search in Google Scholar

[11] L.E.J. Brouwer, Uber Abbildung von Mannigfaltigkeiten, Math. Ann., 71 (1912), 97–115.10.1007/BF01456931Search in Google Scholar

[12] F.E. Browder, Fixed point theory and nonlinear problems., Bull. Am. Math. Soc., 9 (1983), 1–39.10.1090/S0273-0979-1983-15153-4Search in Google Scholar

[13] F.E. Browder, Degree of mapping for nonlinear mappings of monotone type., Proc. Nat. Acad. Sci. USA, 80 (1983), 1771–1773.10.1073/pnas.80.6.1771Search in Google Scholar

[14] K.C. Chang, Critical point theory and applications, Shanghai Scientific and Technology Press, Shanghai, 1986 (english).Search in Google Scholar

[15] L. Dingien, P. Harjulehto, P. H¨astö and M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Springer (2011).10.1007/978-3-642-18363-8Search in Google Scholar

[16] G.Dong, Elliptic equations with measure data in Orlicz spaces, Elec. J. of Diff. Equ., 2008 no. 76 (2008), 1–10.Search in Google Scholar

[17] X. L. Fan and D. Zhao, On the Spaces L^p(x)(Ω) and W^m,p(x)(Ω); J. Math. Anal. Appl., 263 (2001), 424–446.10.1006/jmaa.2000.7617Search in Google Scholar

[18] O. Kováčik and J. Rákosník, On spaces L^p(x) and W^1,p(x), Czechoslovak Math. J., 41 (1991), 592–618.10.21136/CMJ.1991.102493Search in Google Scholar

[19] B. Lahmi, E. Azroul and K. El Haiti, Nonlinear degenerated elliptic problems with dual data and nonstandard growth, Math. reports, 20(70)no. 1 (2018), 81–91.Search in Google Scholar

[20] J. Leray and J. Schauder, Topologie et equationes fonctionnelles, Ann. Sci. Ec. Norm. Super., 51 (1934), 45–78.10.24033/asens.836Search in Google Scholar

[21] R. Landes and V. Mustonen, Pseudo-monotne mappings in Orlicz-Sobolev spaces and nonlinear boundary value problems on unbounded domains, J. Math. Anal., 88 (1982), 25–36.10.1016/0022-247X(82)90173-1Search in Google Scholar

[22] M. Ružička, Electrorheological fluids: modeling and mathematical theory, Lecture Notes in Mathematics 1748, Springer-verlag, Berlin (2000).10.1007/BFb0104029Search in Google Scholar