On the Liouville property for fully nonlinear equations
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 2, pp. 219-245. 
@article{AIHPC_2000__17_2_219_0,
     author = {Cutr{\`\i}, Alessandra and Leoni, Fabiana},
     title = {On the {Liouville} property for fully nonlinear equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {219--245},
     publisher = {Gauthier-Villars},
     volume = {17},
     number = {2},
     year = {2000},
     mrnumber = {1753094},
     zbl = {0956.35035},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_2000__17_2_219_0/}
}
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Cutrì, Alessandra; Leoni, Fabiana. On the Liouville property for fully nonlinear equations. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 2, pp. 219-245. http://archive.numdam.org/item/AIHPC_2000__17_2_219_0/

[1] Bahri A., Lions P.L., Solutions of superlinear elliptic equations and their Morse indexes, Comm. Pure Appl. Math. 45 (1992) 1205-1215. | MR | Zbl

[2] Berestycki H., Capuzzo Dolcetta I., Nirenberg L., Problèmes elliptiques indéfinis et théorèmes de Liouville non-linéaires, C. R. Acad. Sci. Paris, Série I 317 (1993) 945-950. | MR | Zbl

[3] Berestycki H., Capuzzo Dolcetta I., Nirenberg L., Superlinear indefinite elliptic problems and nonlinear Liouville theorems, Topol. Methods Nonlinear Anal. 4 (1994) 59-78. | MR | Zbl

[4] Birindelli I., Capuzzo Dolcetta I., Cutrì A., Liouville theorems for semilinear equations on the Heisenberg group, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 14 (3) (1997) 295-308. | EuDML | Numdam | MR | Zbl

[5] Birindelli I., Capuzzo Dolcetta I., Cutrì A., Indefinite semi-linear equations on the Heisenberg group: a priori bounds and existence, Comm. Partial Differential Equations 23 (7-8) (1998) 1123-1157. | MR | Zbl

[6] Birindelli I., Mitidieri E., Liouville theorems for elliptic inequalities and applications, Proc. Royal Soc. Edinburgh 128A (1998) 1217-1247. | MR | Zbl

[7] Caffarelli L.A., Interior a priori estimates for solutions of fully nonlinear equations, Ann. Math. 130 (1989) 189-213. | MR | Zbl

[8] Caffarelli L.A., Cabré X., Fully Nonlinear Elliptic Equations, American Mathematical Society Colloquium Publications, Vol. 43, AMS, Providence, RI, 1995. | MR | Zbl

[9] Capuzzo Dolcetta I., Teoremi di Liouville e stime a priori per equazioni ellittiche semilineari, Rend. Sem. Mat. Fis. Milano, to appear.

[10] Capuzzo Dolcetta I., Cutrì A., On the Liouville property for sub-laplacians, Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4) 25 (1-2) (1997) 239-256. | Numdam | MR | Zbl

[11] Crandall M.G., Ishii H., Lions P.L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992) 1-67. | MR | Zbl

[12] Cutrì A., Problemi semilineari ed integro-differenziali per sublaplaciani, Ph.D. Thesis, Universitá di Roma Tor Vergata, 1997.

[13] Gidas B., Spruck J., A priori bounds for positive solutions of nonlinear elliptic equations, Comm. PDE 8 (1981) 883-901. | MR | Zbl

[14] Gidas B., Spruck J., Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 35 (1981) 525-598. | MR | Zbl

[15] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, Berlin, 1983. | MR | Zbl

[16] Ishii H., Lions P.L., Viscosity solutions of fully nonlinear second order elliptic partial differential equations, J. Differential Equations 83 (1990) 26-78. | MR | Zbl

[17] Hörmander L., Notions of Convexity, Progress in Mathematics, Vol. 127, Birkhäuser, Boston, MA, 1994. | MR | Zbl

[18] Lanconelli E., Uguzzoni F., Asymptotic behaviour and non existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group, Boll. Unione Mat. Ital., Sez B 8 (1) (1998). | MR | Zbl

[19] Leoni F., work in preparation.

[20] Pucci C., Operatori ellittici estremanti, Ann. Mat. Pura Appl. 72 (1966) 141-170. | MR | Zbl

[21] Protter M.H., Weinberger H.F., Maximum Principles in Differential Equations, Prentice Hall, 1967. | MR | Zbl

[22] Ramos M., Terracini S., Troestler C., Problèmes elliptiques surlinéaires avec non-linéarité sans signe défini, C. R. Acad. Sci. Paris, Série I 325 (1997) 283-286. | MR | Zbl

[23] Trudinger N.S., Lectures on nonlinear elliptic equations of second order, in: Lectures in Mathematical Sciences, The University of Tokyo, 1995.

[24] Uguzzoni F., A Liouville-type theorem on halfspaces for the Kohn laplacian, Proc. Amer. Math. Soc. 127 (1) (1999) 117-123. | MR | Zbl

[25] Uguzzoni F., A non existence theorem for a semilinear Dirichlet problem involving critical exponent on halfspaces of the Heisenberg group, NODEA 6 (2) (1999). | MR | Zbl