Existence of Solutions for Some Nonlinear Elliptic Anisotropic Unilateral Problems with Lower Order Terms

[1] Aharouch L, Akdim Y. Strongly Nonlinear Elliptic Unilateral Problems without sign condition and L¹Data. Appl. Anal. (2005); 11-31.10.1155/AAA.2005.11Search in Google Scholar

[2] Akdim Y, Azroul E, Benkirane A. Existence Results for Quasilinear Degenerated Equations Via Strong Convergence of Truncations. Rev. Mat. Complut., (2001) 17; 359–379.10.5209/rev_REMA.2004.v17.n2.16730Search in Google Scholar

[3] Akdim Y, Benkirane A, El Moumni M. Existence results for nonlinear elliptic problems with lower order terms. Int. J. Evol. Equ., (2013) 8; 4: 257–276.Search in Google Scholar

[4] Antontsev S, Chipot M. Anisotropic equations: uniqueness and existence results. Differential Integral Equations (2008) 6; 401–419.Search in Google Scholar

[5] Bendahmane M, Karlsen KH. Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres. Electronic. J. Differential Equations, (2006) 46; 1–30.10.1090/conm/371/06845Search in Google Scholar

[6] Benkirane A, Bennouna J. Existence of entropy solutions for nonlinear problems in Orlicz spaces. Abs. and Apl. Ann., (2002) 7; 85–102.10.1155/S1085337502000751Search in Google Scholar

[7] Benkirane A, Bennouna J. Existence and uniqueness of solution of unilateral problems with L1-data in Orlicz spaces. Ital. J. Pure Appl. Math., (2004) 16; 87-102.Search in Google Scholar

[8] Bénilan P, Boccardo L, Gallouet T, Gariepy R, Pierre M, Vázquez J. An L¹-theory of existence and uniqueness of nonlinear elliptic equations. Ann. Sc. Norm. Sup. Pisa, CL. IV(1995).; 22 : 240–273.Search in Google Scholar

[9] Boccardo L, Some nonlinear Dirichlet problems in L¹involving lower order terms in divergence form. Progress in elliptic and parabolic partial differential equations (Capri, 1994), Pitman Res. Notes Math. Ser., 350, p. 43-57, Longman, Harlow, 1996.Search in Google Scholar

[10] Boccardo L, Gallouët T. Strongly nonlinear elliptic equations having natural growth terms and L¹data. Nonlinear Anal. T.M.A. (1992); 19: 573-578.10.1016/0362-546X(92)90022-7Search in Google Scholar

[11] Boccardo L, Gallouët T, Marcellini P. Anisotropic equations in L¹. Differential Integral Equations (1996) 1; 209–212.Search in Google Scholar

[12] Boccardo L, Gallouët T, Orsina L. Existence and nonexistence of solutions for some nonlinear elliptic equations. J. Anal. Math. (1997) 73; 203–223.10.1007/BF02788144Search in Google Scholar

[13] Boccardo L, Murat F, Puel J.-P. Existence of bounded solution for nonlinear elliptic unilateral problems. Ann. Mat. Pura Appl. (1988) 152; 183–196.10.1007/BF01766148Search in Google Scholar

[14] Di Castro A. Existence and regularity results for anisotropic elliptic problems. Adv. Nonlinear Stud. (2009)9; 367–393.10.1515/ans-2009-0207Search in Google Scholar

[15] Di Castro A. Anisotropic elliptic problems wih natural growth terms. Manuscripta Math. (2011) 135: 521–543 .10.1007/s00229-011-0431-3Search in Google Scholar

[16] Di Nardo R, Feo F. Existence and uniqueness for nonlinear anisotropic elliptic equations. Arch. Math.(2014) 102; 141–153.10.1007/s00013-014-0611-ySearch in Google Scholar

[17] Fragala I, Gazzola F, Kawohl B. Existence and nonexistence results for anisotropic quasilinear elliptic equations. Ann. Inst. H. Poincar Anal. Non Linéaire (2004) 5; 715–734.10.1016/j.anihpc.2003.12.001Search in Google Scholar

[18] Guib O, Mercaldo A. Uniqueness results for noncoercive nonlinear elliptic equations with two lower order terms. Commun. Pure Appl. Anal. (2008) 1; 163–192.10.3934/cpaa.2008.7.163Search in Google Scholar

[19] Leray J., Lions L. Quelques Mthodes de Rsolution des Problmes aux Limites Non linaires. Dunod, Paris, 1968.Search in Google Scholar

[20] J. P. Gossez and V. Mustonen, Variational inequalities in Orlicz-Sobolev spaces, Nonlinear Anal. (1987) 11; 379-492.10.1016/0362-546X(87)90053-8Search in Google Scholar

[21] Li FQ. Anisotropic elliptic equations in L^m. J. Convex Anal. (2001) 2; 417–422.Search in Google Scholar

[22] M.Troisi. Teoremi di inclusione per spazi di Sobolev non isotropi. Ricerche Mat (1969) 18; 3–24.Search in Google Scholar

[23] Yazough C, Azroul E, Redwane H. Existence of solutions for some nonlinear elliptic unilateral problems with measure data. E. J.Q. Theo. of Di. Equations. (2013) 43; 1–21.10.14232/ejqtde.2013.1.43Search in Google Scholar