@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}, pages = {1099--1119}, publisher = {Elsevier}, volume = {26}, number = {4}, year = {2009}, doi = {10.1016/j.anihpc.2008.06.001}, zbl = {1172.35405}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2008.06.001/} }
TY - JOUR AU - Damascelli, Lucio AU - Farina, Alberto AU - Sciunzi, Berardino AU - Valdinoci, Enrico TI - Liouville Results for $m$-Laplace Equations of Lane-Emden-Fowler Type JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 1099 EP - 1119 VL - 26 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2008.06.001/ DO - 10.1016/j.anihpc.2008.06.001 LA - en ID - AIHPC_2009__26_4_1099_0 ER -
%0 Journal Article %A Damascelli, Lucio %A Farina, Alberto %A Sciunzi, Berardino %A Valdinoci, Enrico %T Liouville Results for $m$-Laplace Equations of Lane-Emden-Fowler Type %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 1099-1119 %V 26 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2008.06.001/ %R 10.1016/j.anihpc.2008.06.001 %G en %F 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, Volume 26 (2009) no. 4, pp. 1099-1119. doi : 10.1016/j.anihpc.2008.06.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2008.06.001/
[1] Local and Global Behavior of Solutions of Quasilinear Equations of Emden-Fowler Type, Arch. Rational Mech. Anal. 107 (4) (1989) 293-324. | MR | Zbl
,[2] Nonlinear Elliptic Equations on Compact Riemannian Manifolds and Asymptotics of Emden Equations, Invent. Math. 106 (3) (1991) 489-539. | EuDML | MR | Zbl
, ,[3] D. Castorina, P. Esposito, B. Sciunzi, Degenerate elliptic equations with singular nonlinearities, preprint. | MR | Zbl
[4] Classification of Solutions of Some Nonlinear Elliptic Equations, Duke Math. J. 63 (3) (1991) 615-622. | MR | Zbl
, ,[5] A Strong Comparison Principle for Positive Solutions of Degenerate Elliptic Equations, Differential Integral Equations 13 (4-6) (2000) 721-746. | MR | Zbl
, ,[6] Symmetry of Solutions of P-Laplace Equations in , Adv. Nonlinear Stud. 1 (1) (2001) 40-64. | MR | Zbl
, ,[7] Regularity, Monotonicity and Symmetry of Positive Solutions of M-Laplace Equations, J. Differential Equations 206 (2) (2004) 483-515. | MR | Zbl
, ,[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
, ,[9] Some Notes on the Method of Moving Planes, Bull. Austral. Math. Soc. 46 (3) (1992) 425-434. | MR | Zbl
,[10] On the Regularity of Solutions in the Pucci-Serrin Identity, Calc. Var. Partial Differential Equations 18 (3) (2003) 317-334. | MR | Zbl
, , ,[11] Local Regularity of Weak Solutions of Degenerate Elliptic Equations, Nonlinear Anal. 7 (8) (1983) 827-850. | MR | Zbl
,[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 | Zbl
, ,[13] Further Studies of Emden's and Similar Equations, Quart. J. Math. Oxford Ser. 2 2 (1931) 259-288. | Zbl
,[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
,[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 | Zbl
,[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 | Zbl
[17] Global and Local Behavior of Positive Solutions of Nonlinear Elliptic Equations, Comm. Pure Appl. Math. 34 (4) (1981) 525-598. | MR | Zbl
, ,[18] Global a Priori Bounds for Positive Solutions of Nonlinear Elliptic Equations, Comm. Partial Differential Equations 6 (8) (1981) 883-901. | MR | Zbl
, ,[19] Quasilinear Dirichlet Problems Driven by Positive Sources, Arch. Rational Mech. Anal. 49 (1-2) (1972/73) 241-269. | MR | Zbl
, ,[20] Boundary Value Problems for Some Degenerate-Elliptic Operators, Ann. Mat. Pura Appl. (4) 80 (1968) 1-122. | MR | Zbl
, ,[21] Boundary Regularity for Solutions of Degenerate Elliptic Equations, Nonlinear Anal. 12 (11) (1988) 1203-1219. | MR | Zbl
,[22] On the Eigenfunctions of the Equation , Dokl. Akad. Nauk SSSR 165 (1965) 36-39. | MR | Zbl
,[23] A General Variational Identity, Indiana Univ. Math. J. 35 (3) (1986) 681-703. | MR | Zbl
, ,[24] The Strong Maximum Principle Revisited, J. Differential Equations 196 (1) (2004) 1-66. | MR | Zbl
, ,[25] Local Behavior of Solutions of Quasi-Linear Elliptic Equations, Acta Math. 111 (1964) 247-302. | MR | Zbl
,[26] Cauchy-Liouville and Universal Boundedness Theorems for Quasilinear Elliptic Equations and Inequalities, Acta Math. 189 (2002). | MR | Zbl
, ,[27] Regularity for a More General Class of Quasilinear Elliptic Equations, J. Differential Equations 51 (1984) 126-150. | MR | Zbl
,[28] A Strong Maximum Principle for Some Quasilinear Elliptic Equations, Appl. Math. Optim. (1984) 191-202. | MR | Zbl
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