Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
ESAIM: Control, Optimisation and Calculus of Variations, Tome 3 (1998), pp. 361-380.
@article{COCV_1998__3__361_0,
     author = {Casas, E. and Kavian, O. and Puel, J.-P.},
     title = {Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {361--380},
     publisher = {EDP-Sciences},
     volume = {3},
     year = {1998},
     zbl = {0911.49003},
     mrnumber = {1660947},
     language = {en},
     url = {http://archive.numdam.org/item/COCV_1998__3__361_0/}
}
TY  - JOUR
AU  - Casas, E.
AU  - Kavian, O.
AU  - Puel, J.-P.
TI  - Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 1998
DA  - 1998///
SP  - 361
EP  - 380
VL  - 3
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/COCV_1998__3__361_0/
UR  - https://zbmath.org/?q=an%3A0911.49003
UR  - https://www.ams.org/mathscinet-getitem?mr=1660947
LA  - en
ID  - COCV_1998__3__361_0
ER  - 
Casas, E.; Kavian, O.; Puel, J.-P. Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 3 (1998), pp. 361-380. http://archive.numdam.org/item/COCV_1998__3__361_0/

[1] H. Amann: On the number of solutions of nonlinear equations in ordered Banach spaces. J. Func. Anal., 11 1972, 346-384. | MR 358470 | Zbl 0244.47046

[2] L. Boccardo, F. Murat: Almost everywhere convergence of the gradients of solutions to elliptic and parabolie equationsNonlinear Anal., Theory, Methods, Appl., 19 1992, 581-597. | MR 1183665 | Zbl 0783.35020

[3] S. Chandrasekhar: An introduction to the study of stellar structures. Dover Publishing Inc., 1985. | MR 92663 | Zbl 0079.23901

[4] M.G. Grandall, P.H. Rabinowitz: Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems. Arch. Rational Mech. Anal., 58 1975, 207-218. | MR 382848 | Zbl 0309.35057

[5] D.A. Franck-Kamenetskii: Diffusion and heat transfer in chemical kinetics. Second edition, Plenum Press, 1969.

[6] Th. Gallouët, F. Mignot, J.P. Puel: Quelques résultats sur le problème -∆u = λeu. C. R. Acad. Sci. Paris, 307, série I, 1988, 289-292. | MR 958783 | Zbl 0697.35048

[7] I.M. Gelfand: Some problems in the theory of quasi-linear equations. Uspekhi Mat. Nauk, (N.S.), 14 (86), 1959, 87-158 (in russian); Amer. Math. Soc. Transl, (Ser. 2), 29, 1963, 289-292. | MR 110868

[8] F. Mignot, J.P. Puel: Sur une classe de problèmes non linéaires avec nonlinéarité positive, croissante, convexe. Comm. PDE, 5 (8), 1980, 791-836. | MR 583604 | Zbl 0456.35034

[9] F. Mignot, J.P. Puel: Solution singulière radiale de -∆u = λeu. C. R. Acad. Sci. Paris, 307, série I, 1988, 379-382. | MR 965802 | Zbl 0683.35032

[10] D.H. Sattinger: Monotone methods in nonlinear elliptic and parabolic boundary value problems. Indiana Univ. Math. J., 21 1972, 979-1000. | MR 299921 | Zbl 0223.35038

[11] J.C. Saut, B. Scheurer: Sur l'unicité du problème de cauchy et le prolongement unique pour des équations elliptiques à coefficients non localement bornés. J. Diff. Eq., 43 1982, 28-43. | MR 645635 | Zbl 0431.35017

[12] G. Stampacchia: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier, 15 1965, 189-258. | Numdam | MR 192177 | Zbl 0151.15401