Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems

Akdim, Youssef; Azroul, Elhoussine; Benkirane, Abdelmoujib

doi:10.5802/ambp.166

Akdim, Youssef ; Azroul, Elhoussine ; Benkirane, Abdelmoujib

Annales Mathématiques Blaise Pascal, Tome 10 (2003) no. 1, pp. 1-20.

Résumé

An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form $A u + g (x, u, \nabla u)$ , 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 $W^{- 1, p^{'}} (Ω, w^{*})$ .

MR 1990009 | Zbl 02068409 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/ambp.166

BibTeX
RIS

@article{AMBP_2003__10_1_1_0,
     author = {Akdim, Youssef and Azroul, Elhoussine and Benkirane, Abdelmoujib},
     title = {Existence of {Solution} for {Quasilinear} {Degenerated} {Elliptic} {Unilateral} {Problems}},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {1--20},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {10},
     number = {1},
     year = {2003},
     doi = {10.5802/ambp.166},
     mrnumber = {1990009},
     zbl = {02068409},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/ambp.166/}
}

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JO  - Annales Mathématiques Blaise Pascal
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EP  - 20
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PB  - Annales mathématiques Blaise Pascal
UR  - http://www.numdam.org/articles/10.5802/ambp.166/
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DO  - 10.5802/ambp.166
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Akdim, Youssef; Azroul, Elhoussine; Benkirane, Abdelmoujib. 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. http://www.numdam.org/articles/10.5802/ambp.166/

Bibliographie
Cité par

[1] Akdim, Y.; Azroul, E.; Benkirane, A. Existence of solutions for quasilinear degenerated elliptic equations, Electronic J. Diff. Eqns., Volume 2001 (2001) no. 71, pp. 1-19 | MR 1872050 | Zbl 0988.35065

[2] Benkirane, A.; Elmahi, A. Strongly nonlinear elliptic unilateral problem having natural growth terms and $L^{1}$ data, Rendiconti di Matematica, Volume 18 (1998), pp. 289-303 | MR 1659834 | Zbl 0918.35059

[3] Bensoussan, A.; Boccardo, L.; Murat, F. 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 963104 | Zbl 0696.35042

[4] Drabek, P.; Kufner, A.; Mustonen, V. Pseudo-monotonicity and degenerated or singular elliptic operators, Bull. Austral. Math. Soc., Volume 58 (1998), pp. 213-221 | Article | MR 1642031 | Zbl 0913.35051

[5] Drabek, P.; Kufner, A.; Nicolosi, F. Quasilinear elliptic equations with degenerations and singularities, De Gruyter Series in Nonlinear Analysis and Applications, New York, 1997 | MR 1460729 | Zbl 0894.35002

[6] Drabek, P.; Nicolosi, F. Existence of Bounded Solutions for Some Degenerated Quasilinear Elliptic Equations, Annali di Mathematica pura ed applicata, Volume CLXV (1993), pp. 217-238 | Article | MR 1271420 | Zbl 0806.35047

[7] Lions, J.L. Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969 | MR 259693 | Zbl 0189.40603

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