Existence of a weak bounded solution for nonlinear degenerate elliptic equations in Musielak-Orlicz spaces

[1] R. Adams; Sobolev spaces, Academic Press Inc, New York, (1975).Search in Google Scholar

[2] Y. Ahmida, I. Chlebicka, P. Gwiazda, A. Youssfi, Gossez’s approximation theorems in Musielak-Orlicz-Sobolev spaces, J. Funct. Anal. (2018), https://doi.org/10.1016/j.jfa.2018.05.01510.1016/j.jfa.2018.05.015Search in Google Scholar

[3] Y. Ahmida, A. Youssfi, Poincaré-type inequalities in Musielak spaces, Annales Academi Scientiarum Fennic Mathematica, (2019), https://doi.org/10.5186/aasfm.2019.446810.5186/aasfm.2019.4468Search in Google Scholar

[4] A. Alvino, L. Boccardo, V. Ferone, L. Orsina, G. Trombetti; Existence results for nonlinear elliptic equations with degenerate coercivity, Ann. Mat. Pura Appl., IV. Ser. 182, No.1, (2003), 53-79.10.1007/s10231-002-0056-ySearch in Google Scholar

[5] M. Ait Khellou, A. Benkirane, S.M. Douiri; Existence of solutions for elliptic equations having natural growth terms in Musielak-Orlicz spaces. J. Math. Comput. Sci. 4(4), 665688 (2014)Search in Google Scholar

[6] A. Alvino, V. Ferone, G. Trombetti; A priori estimates for a class of non uniformly elliptic equations, Atti Semin. Mat. Fis. Univ. Modena 46-suppl., (1998), 381-391.Search in Google Scholar

[7] A. Benkirane, M. Sidi El Vally(Ould Mohameden Val); Variational inequalities in Musielak-Orlicz-Sobolev spaces, Bull. Belg. Math.Soc. Simon Stevin, Vol 21, No.5 (2014), pp. 787-811.Search in Google Scholar

[8] A. Benkirane, M. Sidi El Vally(Ould Mohameden Val); An existence result for nonlinear elliptic equations in Musielak-Orlicz-Sobolev spaces, Bull. Belg. Math.Soc. Simon Stevin 20(2013), No. 1, 57-75.Search in Google Scholar

[9] L. Boccardo, A. Dall’Aglio, L. Orsina; Existence and regularity results for some elliptic equations with degenerate coercivity. Atti Semin. Mat. Fis. Univ. Modena 46-suppl., (1998), 51-81.Search in Google Scholar

[10] M. Bourahma, A. Benkirane, J. Bennouna, Existence of renormalized solutions for some nonlinear elliptic equations in Orlicz spaces, J. Rend. Circ. Mat. Palermo, II. Ser (2019). https://doi.org/10.1007/s12215-019-00399-z10.1007/s12215-019-00399-zSearch in Google Scholar

[11] I. Chlebicka, P. Gwiazda and A. Zatorska Goldstein, Well-posedness of parabolic equations in the non-reflexive and anisotropic Musielak-Orlicz spaces in the class of renormalized solutions, arXiv:1707.06097v4 [math.AP] 13 Apr 2018.10.1016/j.jde.2018.07.020Search in Google Scholar

[12] J. P. Gossez; A strongly nonlinear elliptic problem in Orlicz-Sobolev spaces, Proc. Sympos. Pure Math. 45, Amer. Math. Soc., (1986), 455-462.10.1090/pspum/045.1/843579Search in Google Scholar

[13] J. P. Gossez, Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients, Trans. Amer. Math. soc. 190, (1974), 163-205.10.1090/S0002-9947-1974-0342854-2Search in Google Scholar

[14] P. Gwiazda, I. Skrzypczak, A. Zatorska.Goldstein, Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space, J. Differential Equations 264 (2018) 341377.Search in Google Scholar

[15] M. Krasnosel’skii, Ya. Rutikii; Convex functions and Orlicz spaces, Groningen, Nordhooff (1969).Search in Google Scholar

[16] J. Musielak; Orlicz spaces and modular spaces, Lecture Note in Mahtematics, 1034, Springer, Berlin, 1983.10.1007/BFb0072210Search in Google Scholar

[17] G. Talenti; Nonlinear elliptic equations, Rearrangements of functions and Orlicz spaces, Ann. Mat. Pura Appl., IV. Ser. 120, (1979), 159-184.10.1007/BF02411942Search in Google Scholar

[18] G. Talenti; Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa (4) 3, (1976), 697-718.Search in Google Scholar

[19] A. Youssfi; Existence of bounded solution for nonlinear degenerate elliptic equations in Orlicz spaces, Electronic Journal of Differential Equations, Vol. 2007(2007), No. 54, pp. 1-13.Search in Google Scholar