Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems

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

Annales mathématiques Blaise Pascal (2003)

  • Volume: 10, Issue: 1, page 1-20
  • ISSN: 1259-1734

Abstract

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An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form A u + 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 * ) .

How to cite

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Akdim, Youssef, Azroul, Elhoussine, and Benkirane, Abdelmoujib. "Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems." Annales mathématiques Blaise Pascal 10.1 (2003): 1-20. <http://eudml.org/doc/10483>.

@article{Akdim2003,
abstract = {An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form $Au+g(x,u,\nabla u)$, where $A$ is a Leray-Lions operator from $W_0^\{1,p\}(\Omega ,w)$ into its dual, while $g(x,s,\xi )$ is a nonlinear term which has a growth condition with respect to $\xi $ and no growth with respect to $s$, but it satisfies a sign condition on $s$, the second term belongs to $W^\{-1,p^\{\prime\}\}(\Omega ,w^*)$.},
affiliation = {Département de Mathématiques et Informatique Faculté des Sciences Dhar-Mahraz B.P 1796 Atlas Fès. MAROC; Département de Mathématiques et Informatique Faculté des Sciences Dhar-Mahraz B.P 1796 Atlas Fès. MAROC; Département de Mathématiques et Informatique Faculté des Sciences Dhar-Mahraz B.P 1796 Atlas Fès. MAROC},
author = {Akdim, Youssef, Azroul, Elhoussine, Benkirane, Abdelmoujib},
journal = {Annales mathématiques Blaise Pascal},
keywords = {quasilinear degenerated elliptic BVP; unilateral boundary condition; a priori estimates},
language = {eng},
month = {1},
number = {1},
pages = {1-20},
publisher = {Annales mathématiques Blaise Pascal},
title = {Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems},
url = {http://eudml.org/doc/10483},
volume = {10},
year = {2003},
}

TY - JOUR
AU - Akdim, Youssef
AU - Azroul, Elhoussine
AU - Benkirane, Abdelmoujib
TI - Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems
JO - Annales mathématiques Blaise Pascal
DA - 2003/1//
PB - Annales mathématiques Blaise Pascal
VL - 10
IS - 1
SP - 1
EP - 20
AB - An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form $Au+g(x,u,\nabla u)$, where $A$ is a Leray-Lions operator from $W_0^{1,p}(\Omega ,w)$ into its dual, while $g(x,s,\xi )$ is a nonlinear term which has a growth condition with respect to $\xi $ and no growth with respect to $s$, but it satisfies a sign condition on $s$, the second term belongs to $W^{-1,p^{\prime}}(\Omega ,w^*)$.
LA - eng
KW - quasilinear degenerated elliptic BVP; unilateral boundary condition; a priori estimates
UR - http://eudml.org/doc/10483
ER -

References

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  1. Y. Akdim, E. Azroul, A. Benkirane, Existence of solutions for quasilinear degenerated elliptic equations, Electronic J. Diff. Eqns. 2001 (2001), 1-19 Zbl0988.35065MR1872050
  2. A. Benkirane, A. Elmahi, Strongly nonlinear elliptic unilateral problem having natural growth terms and L 1 data, Rendiconti di Matematica 18 (1998), 289-303 Zbl0918.35059MR1659834
  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 5 (1988), 347-364 Zbl0696.35042MR963104
  4. P. Drabek, A. Kufner, V. Mustonen, Pseudo-monotonicity and degenerated or singular elliptic operators, Bull. Austral. Math. Soc. 58 (1998), 213-221 Zbl0913.35051MR1642031
  5. P. Drabek, A. Kufner, F. Nicolosi, Quasilinear elliptic equations with degenerations and singularities, (1997), De Gruyter Series in Nonlinear Analysis and Applications, New York Zbl0894.35002MR1460729
  6. P. Drabek, F. Nicolosi, Existence of Bounded Solutions for Some Degenerated Quasilinear Elliptic Equations, Annali di Mathematica pura ed applicata CLXV (1993), 217-238 Zbl0806.35047MR1271420
  7. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, (1969), Dunod, Paris Zbl0189.40603MR259693

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