On a nonlinear elliptic problems having large monotonocity with L¹-data in weighted Orlicz-Sobolev spaces

[1] R. Adams; Sobolev spaces, Academic Press, NewYork 1975.Search in Google Scholar

[2] L. Aharouch, E. Azroul and M. Rhoudaf, Nonlinear unilateral problems in Orlicz spaces, Applicationes Mathematicae 33 (2006), no. 2, 217-241.10.4064/am33-2-6Search in Google Scholar

[3] E. Azroul and A. Benkirane: Existence result for a second order nonlinear degenerate elliptic equation in weighted Orlicz-Sobolev spaces. Lecture Note in Pure and Applied Mathematics, Vol 229,pp 111-124 (2002).Search in Google Scholar

[4] Aissaoui Fqayeh, A. Benkirane, A. El Moumni, M. and Youssfi, A. Existence of renormalized solutions for some strongly nonlinear elliptic equations in Orlicz spaces, Georgian Math. J.22 (3), (2015), 305–321.10.1515/gmj-2015-0038Search in Google Scholar

[5] A. Benkirane, Y. El Hadfi, M. El Moumni; Renormalized solutions for nonlinear parabolic problems with L¹-data in Orlicz-Sobolev spaces, Bol. Soc. Parana. Mat. 35(3) (2017), no. 1, 57–84.10.5269/bspm.v35i1.27425Search in Google Scholar

[6] A. Benkirane, A. Elmahi; Almost everywhere convergence of the gradient of solutions to elliptic equations in Orlicz spaces, Nonlinear Anal. T.M.A. 28(11)(1997) 1769–1784.10.1016/S0362-546X(96)00017-XSearch in Google Scholar

[7] A. Benkirane, A. Elmahi; An existence theorem for a strongly nonlinear elliptic problem in Orlicz spaces, Nonlinear Anal. 36(1) (1999), Ser. A: Theory Methods, 11–24.10.1016/S0362-546X(97)00612-3Search in Google Scholar

[8] Brezis, H. Operateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland Mathematics Studies, No. 5. Notas de Matemtica (50). North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973, MR 50 ≠ 1060 Zbl 252.47055.Search in Google Scholar

[9] Browder, F.E. Existence theorems for nonlinear partial differential equations, Global Analysis (Berkeley, 1968), Proc. Sympos. Pure Math., no. XVI, AMS, Providence, 1970, pp. 1–60, MR 42 6= 4855.10.1090/pspum/016/0269962Search in Google Scholar

[10] Chen, Y, Levine, S, Rao, R. Variable exponent, linear growth functionals in image restoration. SIAM J. Appl. Math.66, 1383–1406 (2006).10.1137/050624522Search in Google Scholar

[11] Diening, L, Harjulehto, P, Hasto, P, Ruzuka, M. Lebesgue and Sobolev Spaces with Variable Exponents. Springer, Berlin (2011).10.1007/978-3-642-18363-8Search in Google Scholar

[12] I. Ekland, R. Temam; Analyse convexe et problèmes variationnels, (French) Collection Études Mathématiques. Dunod; Gauthier-Villars, Paris-Brussels-Montreal, Que., 1974. x+340 pp. 49–02.Search in Google Scholar

[13] M. A. Krasnosel’skii, Ja. B. Rutickii; Convex functions and Orlicz spaces, Translated from the first Russian edition by Leo F. Boron. P. Noordhoff Ltd., Groningen 1961 xi+249 pp. 46–35.Search in Google Scholar

[14] Leray, J. and Lions, J.L. Quelques rêsultats de visik sur les problèmes elliptiques semilinèaires par les mèthodes de Minty et Browder, Bull. Soc. Math. France,93(1965), 97–107.10.24033/bsmf.1617Search in Google Scholar

[15] Li, F, Li, Z, Pi, L. Variable exponent functionals in image restoration. Appl. Math. Comput. 216, 870-882 (2010).10.1016/j.amc.2010.01.094Search in Google Scholar

[16] Lions, J.L. Quelques mèthodes de rèsolution des problèmes aux limites non linèaire, Dunod et Gauthier Villars, Paris, 1969.Search in Google Scholar

[17] Minty, G.J. On a monotonicity method for the solution of non-linear equations in Banach spaces, Proc. Nat. Acad. Sci. U.S.A.50(1963), 1038–1041.10.1073/pnas.50.6.103822126916578554Search in Google Scholar

[18] Minty, G.J. Monotone (nonlinear) operators in Hilbert space, Duke Math. J.291962.Search in Google Scholar

[19] Musielak, J. Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034, Springer, Berlin, 1983.10.1007/BFb0072210Search in Google Scholar

[20] A. Youssfi, A. Benkirane, M. El Moumni; Bounded solutions of unilateral problems for strongly nonlinear equations in Orlicz spaces, Electron. J. Qual. Theory Differ. Equ. No.21(2013), 25 pp.10.14232/ejqtde.2013.1.21Search in Google Scholar

[21] A. Benkirane, M. El Moumni, K. Kouhaila; Solvability of strongly nonlinear elliptic variational problems in weighted Orlicz?Sobolev spaces, SeMA Journal Boletin de la Sociedad Espaola de Matemtica Aplicada (accepted),Search in Google Scholar