On a non linear partial differential equation having natural growth terms and unbounded solution
Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) no. 4, pp. 347-364. 
@article{AIHPC_1988__5_4_347_0,
     author = {Bensoussan, A. and Boccardo, L. and Murat, F.},
     title = {On a non linear partial differential equation having natural growth terms and unbounded solution},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {347--364},
     publisher = {Gauthier-Villars},
     volume = {5},
     number = {4},
     year = {1988},
     mrnumber = {963104},
     zbl = {0696.35042},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1988__5_4_347_0/}
}
TY  - JOUR
AU  - Bensoussan, A.
AU  - Boccardo, L.
AU  - Murat, F.
TI  - On a non linear partial differential equation having natural growth terms and unbounded solution
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1988
SP  - 347
EP  - 364
VL  - 5
IS  - 4
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPC_1988__5_4_347_0/
LA  - en
ID  - AIHPC_1988__5_4_347_0
ER  - 
%0 Journal Article
%A Bensoussan, A.
%A Boccardo, L.
%A Murat, F.
%T On a non linear partial differential equation having natural growth terms and unbounded solution
%J Annales de l'I.H.P. Analyse non linéaire
%D 1988
%P 347-364
%V 5
%N 4
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPC_1988__5_4_347_0/
%G en
%F AIHPC_1988__5_4_347_0
Bensoussan, A.; Boccardo, L.; Murat, F. On a non linear partial differential equation having natural growth terms and unbounded solution. Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) no. 4, pp. 347-364. http://archive.numdam.org/item/AIHPC_1988__5_4_347_0/

[1] H. Amann and M.G. Crandall, On Some Existence Theorems for Semi Linear Elliptic Equations, Indiana Univ. Math. J., Vol. 27, 1978, pp. 779-790. | MR | Zbl

[2] A. Bensoussan and J. Frehse, Nonlinear Elliptic Systems in Stochastic Game Theory, J. Reine Ang. Math., Vol. 350, 1984, pp. 23-67. | MR | Zbl

[3] A. Bensoussan, J. Frehse and U. Mosco, A Stochastic Impulse Control Problem with Quadratic Growth Hamiltonian and the Corresponding Quasi Variational Inequality, J. Reine Ang. Math., Vol. 331, 1982, pp. 124-145. | MR | Zbl

[4] L. Boccardo and D. Giachetti, Strongly Non Linear Unilateral Problems, Appl. Mat. Opt., Vol. 9, 1983, pp. 291-301. | MR | Zbl

[5] L. Boccardo and D. Giachetti, Alcune osservazioni sulla regolarità delle soluzioni di problemi fortemente non lineari e applicazioni, Ricerche di Matematica, Vol. 34, 1985, pp. 309-323. | MR | Zbl

[6] L. Boccardo, D. Giachetti and F. Murat, On a Generalization of a Theorem of Brezis-Browder, 1984, unpublished.

[7] L. Boccardo, F. Murat and J.P. Puel, Existence de solutions non bornées pour certaines équations quasi-linéaires, Portugaliae Math., Vol. 41, 1982, pp. 507-534. | MR | Zbl

[8] L. Boccardo, F. Murat and J.P. Puel, Existence de solutions faibles pour des équations elliptiques quasi-linéaires à croissance quadratique, Nonlinear Partial Differ ential Equations and Their Applications, Collège de France Seminar, Vol. IV, J. L. LIONS and H. BREZIS Eds., Research Notes in Mathematics, No. 84, Pitman, London, 1983, pp. 19-73. | MR | Zbl

[9] L. Boccardo, F. Murat and J.P. Puel, Résultats d'existence pour certains problèmes elliptiques quasi-linéaires, Ann. Sc. Norm. Sup. Pisa, Vol. 11, 1984, pp. 213-235. | Numdam | MR | Zbl

[10] L. Boccardo, F. Murat and J.P. Puel, Existence of Bounded Solutions for Non Linear Elliptic Unilateral Problems, Annali di Mat. Pura Appl., (to appear). | Zbl

[11] H. Brezis and F.E. Browder, Some Properties of Higher Order Sobolev Spaces, J. Math. Pures Appl., Vol. 61, 1982, pp. 245-259. | MR | Zbl

[12] F.E. Browder, Existence Theorems for Non Linear Partial Differential Equations, Proceedings of Symposia in Pure Mathematics, Vol. 16, S. S. CHERN and S. SMALE Eds., A.M.S., Providence, 1970, pp. 1-60. | MR | Zbl

[13] T. Del Vecchio, Strongly Non Linear Problems with Gradient Dependent Lower Order Non Linearity, Nonlinear Anal. T.M.A., Vol. 11, 1987, pp. 5-15. | MR | Zbl

[14] J. Frehse, A Refinement of Rellich's Theorem, Rendiconti di Matematica, (to appear). | Zbl

[15] P. Hess, Variational Inequalities for Strongly Non Linear Elliptic Operators, J. Math. Pures Appl., Vol. 52, 1973, pp. 285-298. | MR | Zbl

[16] R. Landes, Solvability of Perturbated Elliptic Equations with Critical Growth Exponent for the Gradient, Preprint. | MR

[17] J. Leray and J.L. Lions, Quelques résultats de Visik sur les problèmes elliptiques non linéaires par la méthode de Minty-Browder, Bull. Soc. Math. France, Vol. 93, 1965, pp. 97-107. | Numdam | MR | Zbl

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

[19] J.M. Rakotoson and R. Temam, Relative Rearrangement in Quasilinear Variational Inequalities, Indiana Univ. Math. J., 36, 1987, pp. 757-810. | MR

[20] J.R.L. Webb, Boundary Value Problems for Strongly Non Linear Elliptic Equations, J. London Math. Soc., Vol. 21, 1980, pp. 123-132. | MR | Zbl