In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type where is a Leray-Lions operator and is a Carathéodory function having natural growth with respect to and satisfying the sign condition. The second term is such that, and .
@article{AMBP_2004__11_1_47_0, author = {Lahsen Aharouch and Youssef Akdim}, title = {Existence of solutions of degenerated unilateral problems with $L^1$ data}, journal = {Annales Math\'ematiques Blaise Pascal}, pages = {47--66}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {11}, number = {1}, year = {2004}, doi = {10.5802/ambp.185}, mrnumber = {2077238}, zbl = {02207858}, language = {en}, url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.185/} }
TY - JOUR TI - Existence of solutions of degenerated unilateral problems with $L^1$ data JO - Annales Mathématiques Blaise Pascal PY - 2004 DA - 2004/// SP - 47 EP - 66 VL - 11 IS - 1 PB - Annales mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.185/ UR - https://www.ams.org/mathscinet-getitem?mr=2077238 UR - https://zbmath.org/?q=an%3A02207858 UR - https://doi.org/10.5802/ambp.185 DO - 10.5802/ambp.185 LA - en ID - AMBP_2004__11_1_47_0 ER -
Lahsen Aharouch; Youssef Akdim. Existence of solutions of degenerated unilateral problems with $L^1$ data. Annales Mathématiques Blaise Pascal, Volume 11 (2004) no. 1, pp. 47-66. doi : 10.5802/ambp.185. https://ambp.centre-mersenne.org/articles/10.5802/ambp.185/
[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] Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems, Annale Mathématique Blaise Pascal, Volume 10 (2003), pp. 1-20 | Article | Numdam | MR: 1990009 | Zbl: 1050.35022
[3] Strongly nonlinear degenerated unilateral problems with data, Electronic J. Diff. Eqns. (Conf. 09. 2002), pp. 46-64 | Zbl: 1034.35050
[4] An -theory of existence and uniqueness of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa, Volume 22 (1995), pp. 240-273 | Numdam | MR: 1354907
[5] Non-linear Elliptic Equations with right hand side Measures, commun. In partial Differential Equations, Volume 17 (1992), pp. 641-655 | MR: 1163440 | Zbl: 0812.35043
[6] Strongly non-linear Elliptic Equations having natural growth and data, Nonlinear Anal., Volume 19 (1992), pp. 573-578 | Article | MR: 1183664 | Zbl: 0795.35031
[7] A unified presentation of tow existence results for problems with natural growth, in : Progress in Partial Differential Equations : The Metz Surveys 2, M. Chipot (ed), Pitman Res. Notes Math. Ser. 296, Longman (1993), pp. 127-137 | MR: 1248641 | Zbl: 0806.35033
[8] Existence of bounded solutions for nonlinear elliptic unilateral problems, Ann. Math. Pura Appl., Volume 152 (1988), pp. 183-196 | Article | MR: 980979 | Zbl: 0687.35042
[9] Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup Pisa Cl. Sci, Volume 12 (1999) no. 4, pp. 741-808 | Numdam | MR: 1760541 | Zbl: 0958.35045
[10] Nonlinear elliptic equations, singular and degenerate cases, University of West Bohemia, 1996
[11] Unilateral elleptic problems in with natural growth terms (To appear Nonlinear and convex analysis) | MR: 2101516 | Zbl: 1097.35062
[12] Existence for elliptic equations in having lower order terms with natural growth, Portugal. Math., Volume 57 (2000), pp. 179-190 | MR: 1759814 | Zbl: 0963.35068
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