An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form , where is a Leray-Lions operator from into its dual, while is a nonlinear term which has a growth condition with respect to and no growth with respect to , but it satisfies a sign condition on , the second term belongs to .
@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}, zbl = {02068409}, mrnumber = {1990009}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ambp.166/} }
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 PY - 2003 SP - 1 EP - 20 VL - 10 IS - 1 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.166/ DO - 10.5802/ambp.166 LA - en ID - AMBP_2003__10_1_1_0 ER -
%0 Journal Article %A Akdim, Youssef %A Azroul, Elhoussine %A Benkirane, Abdelmoujib %T Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems %J Annales mathématiques Blaise Pascal %D 2003 %P 1-20 %V 10 %N 1 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.166/ %R 10.5802/ambp.166 %G en %F AMBP_2003__10_1_1_0
Akdim, Youssef; Azroul, Elhoussine; Benkirane, Abdelmoujib. Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems. Annales mathématiques Blaise Pascal, Volume 10 (2003) no. 1, pp. 1-20. doi : 10.5802/ambp.166. http://www.numdam.org/articles/10.5802/ambp.166/
[1] Existence of solutions for quasilinear degenerated elliptic equations, Electronic J. Diff. Eqns., Volume 2001 (2001) no. 71, pp. 1-19 | MR | Zbl
[2] Strongly nonlinear elliptic unilateral problem having natural growth terms and data, Rendiconti di Matematica, Volume 18 (1998), pp. 289-303 | MR | Zbl
[3] 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] Pseudo-monotonicity and degenerated or singular elliptic operators, Bull. Austral. Math. Soc., Volume 58 (1998), pp. 213-221 | DOI | MR | Zbl
[5] Quasilinear elliptic equations with degenerations and singularities, De Gruyter Series in Nonlinear Analysis and Applications, New York, 1997 | MR | Zbl
[6] 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] Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969 | MR | Zbl
Cited by Sources: