@article{AIHPC_2009__26_4_1099_0, author = {Damascelli, Lucio and Farina, Alberto and Sciunzi, Berardino and Valdinoci, Enrico}, title = {Liouville Results for $m$-Laplace Equations of Lane-Emden-Fowler Type}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {26}, year = {2009}, pages = {1099-1119}, doi = {10.1016/j.anihpc.2008.06.001}, zbl = {1172.35405}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_4_1099_0} }
Damascelli, Lucio; Farina, Alberto; Sciunzi, Berardino; Valdinoci, Enrico. Liouville Results for $m$-Laplace Equations of Lane-Emden-Fowler Type. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 1099-1119. doi : 10.1016/j.anihpc.2008.06.001. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_4_1099_0/
[1] Local and Global Behavior of Solutions of Quasilinear Equations of Emden-Fowler Type, Arch. Rational Mech. Anal. 107 (4) (1989) 293-324. | MR 1004713 | Zbl 0696.35022
,[2] Nonlinear Elliptic Equations on Compact Riemannian Manifolds and Asymptotics of Emden Equations, Invent. Math. 106 (3) (1991) 489-539. | MR 1134481 | Zbl 0755.35036
, ,[3] D. Castorina, P. Esposito, B. Sciunzi, Degenerate elliptic equations with singular nonlinearities, preprint. | MR 2471138 | Zbl 1168.35020
[4] Classification of Solutions of Some Nonlinear Elliptic Equations, Duke Math. J. 63 (3) (1991) 615-622. | MR 1121147 | Zbl 0768.35025
, ,[5] A Strong Comparison Principle for Positive Solutions of Degenerate Elliptic Equations, Differential Integral Equations 13 (4-6) (2000) 721-746. | MR 1750048 | Zbl 0973.35077
, ,[6] Symmetry of Solutions of P-Laplace Equations in , Adv. Nonlinear Stud. 1 (1) (2001) 40-64. | MR 1850203 | Zbl 0998.35016
, ,[7] Regularity, Monotonicity and Symmetry of Positive Solutions of M-Laplace Equations, J. Differential Equations 206 (2) (2004) 483-515. | MR 2096703 | Zbl 1108.35069
, ,[8] Harnack Inequalities, Maximum and Comparison Principles, and Regularity of Positive Solutions of M-Laplace Equations, Calc. Var. Partial Differential Equations 25 (2) (2006) 139-159. | MR 2188744 | Zbl pre05014199
, ,[9] Some Notes on the Method of Moving Planes, Bull. Austral. Math. Soc. 46 (3) (1992) 425-434. | MR 1190345 | Zbl 0777.35005
,[10] On the Regularity of Solutions in the Pucci-Serrin Identity, Calc. Var. Partial Differential Equations 18 (3) (2003) 317-334. | MR 2018671 | Zbl 1046.35039
, , ,[11] Local Regularity of Weak Solutions of Degenerate Elliptic Equations, Nonlinear Anal. 7 (8) (1983) 827-850. | MR 709038 | Zbl 0539.35027
,[12] Existence and Nonexistence Results for Semilinear Elliptic Problems in Unbounded Domains, Proc. Roy. Soc. Edinburgh Sect. A 93 (1-2) (1982/83) 1-14. | MR 688279 | Zbl 0506.35035
, ,[13] Further Studies of Emden's and Similar Equations, Quart. J. Math. Oxford Ser. 2 2 (1931) 259-288. | Zbl 0003.23502
,[14] Liouville-Type Results for Solutions of on Unbounded Domains of , C. R. Math. Acad. Sci. Paris, Ser. I 341 (7) (2005) 415-418. | MR 2168740 | Zbl pre02217869
,[15] On the Classification of Solutions of the Lane-Emden Equation on Unbounded Domains of , J. Math. Pures Appl. 87 (5) (2007) 537-561. | MR 2322150 | Zbl 1143.35041
,[16] A. Farina, B. Sciunzi, E. Valdinoci, Bernstein and De Giorgi type problems: New results via a geometric approach, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2008), in press. | Numdam | MR 2483642 | Zbl 1180.35251
[17] Global and Local Behavior of Positive Solutions of Nonlinear Elliptic Equations, Comm. Pure Appl. Math. 34 (4) (1981) 525-598. | MR 615628 | Zbl 0465.35003
, ,[18] Global a Priori Bounds for Positive Solutions of Nonlinear Elliptic Equations, Comm. Partial Differential Equations 6 (8) (1981) 883-901. | MR 619749 | Zbl 0462.35041
, ,[19] Quasilinear Dirichlet Problems Driven by Positive Sources, Arch. Rational Mech. Anal. 49 (1-2) (1972/73) 241-269. | MR 340701 | Zbl 0266.34021
, ,[20] Boundary Value Problems for Some Degenerate-Elliptic Operators, Ann. Mat. Pura Appl. (4) 80 (1968) 1-122. | MR 249828 | Zbl 0185.19201
, ,[21] Boundary Regularity for Solutions of Degenerate Elliptic Equations, Nonlinear Anal. 12 (11) (1988) 1203-1219. | MR 969499 | Zbl 0675.35042
,[22] On the Eigenfunctions of the Equation , Dokl. Akad. Nauk SSSR 165 (1965) 36-39. | MR 192184 | Zbl 0141.30202
,[23] A General Variational Identity, Indiana Univ. Math. J. 35 (3) (1986) 681-703. | MR 855181 | Zbl 0625.35027
, ,[24] The Strong Maximum Principle Revisited, J. Differential Equations 196 (1) (2004) 1-66. | MR 2025185 | Zbl 1109.35022
, ,[25] Local Behavior of Solutions of Quasi-Linear Elliptic Equations, Acta Math. 111 (1964) 247-302. | MR 170096 | Zbl 0128.09101
,[26] Cauchy-Liouville and Universal Boundedness Theorems for Quasilinear Elliptic Equations and Inequalities, Acta Math. 189 (2002). | MR 1946918 | Zbl 1059.35040
, ,[27] Regularity for a More General Class of Quasilinear Elliptic Equations, J. Differential Equations 51 (1984) 126-150. | MR 727034 | Zbl 0488.35017
,[28] A Strong Maximum Principle for Some Quasilinear Elliptic Equations, Appl. Math. Optim. (1984) 191-202. | MR 768629 | Zbl 0561.35003
,