Annales Mathématiques
Blaise Pascal
no. 1
Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems
Youssef Akdim1 ; Elhoussine Azroul1 ; Abdelmoujib Benkirane1
1 Département de Mathématiques et Informatique Faculté des Sciences Dhar-Mahraz B.P 1796 Atlas Fès. MAROC
Annales mathématiques Blaise Pascal, Tome 10 (2003) no. 1, pp. 1-20.

An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form Au+g(x,u,∇u), where A is a Leray-Lions operator from W 0 1,p (Ω,w) into its dual, while g(x,s,ξ) is a nonlinear term which has a growth condition with respect to ξ and no growth with respect to s, but it satisfies a sign condition on s, the second term belongs to W -1,p ′ (Ω,w * ).

DOI : 10.5802/ambp.166

Youssef Akdim 1 ; Elhoussine Azroul 1 ; Abdelmoujib Benkirane 1

1 Département de Mathématiques et Informatique Faculté des Sciences Dhar-Mahraz B.P 1796 Atlas Fès. MAROC 
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Youssef Akdim; Elhoussine Azroul; Abdelmoujib Benkirane. Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems. Annales mathématiques Blaise Pascal, Tome 10 (2003) no. 1, pp. 1-20. doi : 10.5802/ambp.166. https://ambp.centre-mersenne.org/articles/10.5802/ambp.166/

[1] Y. Akdim; E. Azroul; A. Benkirane Existence of solutions for quasilinear degenerated elliptic equations, Electronic J. Diff. Eqns., Volume 2001 (2001) no. 71, pp. 1-19 | MR | Zbl

[2] A. Benkirane; A. Elmahi Strongly nonlinear elliptic unilateral problem having natural growth terms and L 1 data, Rendiconti di Matematica, Volume 18 (1998), pp. 289-303 | MR | Zbl

[3] A. Bensoussan; L. Boccardo; F. Murat On a non linear partial differential equation having natural growth terms and unbounded solution, Ann. Inst. Henri Poincaré, Volume 5 (1988) no. 4, pp. 347-364 | Numdam | MR | Zbl

[4] P. Drabek; A. Kufner; V. Mustonen Pseudo-monotonicity and degenerated or singular elliptic operators, Bull. Austral. Math. Soc., Volume 58 (1998), pp. 213-221 | DOI | MR | Zbl

[5] P. Drabek; A. Kufner; F. Nicolosi Quasilinear elliptic equations with degenerations and singularities, De Gruyter Series in Nonlinear Analysis and Applications, New York, 1997 | MR | Zbl

[6] P. Drabek; F. Nicolosi Existence of Bounded Solutions for Some Degenerated Quasilinear Elliptic Equations, Annali di Mathematica pura ed applicata, Volume CLXV (1993), pp. 217-238 | DOI | MR | Zbl

[7] J.L. Lions Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969 | MR | Zbl

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