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}, mrnumber = {1990009}, zbl = {02068409}, 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 DA - 2003/// SP - 1 EP - 20 VL - 10 IS - 1 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.166/ UR - https://www.ams.org/mathscinet-getitem?mr=1990009 UR - https://zbmath.org/?q=an%3A02068409 UR - https://doi.org/10.5802/ambp.166 DO - 10.5802/ambp.166 LA - en ID - AMBP_2003__10_1_1_0 ER -
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/
[1] 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] Strongly nonlinear elliptic unilateral problem having natural growth terms and data, Rendiconti di Matematica, Volume 18 (1998), pp. 289-303 | MR 1659834 | Zbl 0918.35059
[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 963104 | Zbl 0696.35042
[4] 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] Quasilinear elliptic equations with degenerations and singularities, De Gruyter Series in Nonlinear Analysis and Applications, New York, 1997 | MR 1460729 | Zbl 0894.35002
[6] 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] Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969 | MR 259693 | Zbl 0189.40603
Cité par Sources :