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.
@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
DA  - 2009///
SP  - 1099
EP  - 1119
VL  - 26
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2008.06.001/
UR  - https://zbmath.org/?q=an%3A1172.35405
UR  - https://doi.org/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 https://doi.org/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] Bidaut-Véron M. F., 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] Bidaut-Véron M. F., Véron L., 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] Chen W., Li C., Classification of Solutions of Some Nonlinear Elliptic Equations, Duke Math. J. 63 (3) (1991) 615-622. | MR | Zbl

[5] Cuesta M., Takáč P., A Strong Comparison Principle for Positive Solutions of Degenerate Elliptic Equations, Differential Integral Equations 13 (4-6) (2000) 721-746. | MR | Zbl

[6] Damascelli L., Ramaswamy M., Symmetry of C 1 Solutions of P-Laplace Equations in R N , Adv. Nonlinear Stud. 1 (1) (2001) 40-64. | MR | Zbl

[7] Damascelli L., Sciunzi B., Regularity, Monotonicity and Symmetry of Positive Solutions of M-Laplace Equations, J. Differential Equations 206 (2) (2004) 483-515. | MR | Zbl

[8] Damascelli L., Sciunzi B., 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] Dancer E. N., Some Notes on the Method of Moving Planes, Bull. Austral. Math. Soc. 46 (3) (1992) 425-434. | MR | Zbl

[10] Degiovanni M., Musesti A., Squassina M., On the Regularity of Solutions in the Pucci-Serrin Identity, Calc. Var. Partial Differential Equations 18 (3) (2003) 317-334. | MR | Zbl

[11] Dibenedetto E., C 1+α Local Regularity of Weak Solutions of Degenerate Elliptic Equations, Nonlinear Anal. 7 (8) (1983) 827-850. | MR | Zbl

[12] Esteban M. J., Lions P.-L., 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] Fowler R. H., Further Studies of Emden's and Similar Equations, Quart. J. Math. Oxford Ser. 2 2 (1931) 259-288. | Zbl

[14] Farina A., Liouville-Type Results for Solutions of -Δu=u p-1 u on Unbounded Domains of R N , C. R. Math. Acad. Sci. Paris, Ser. I 341 (7) (2005) 415-418. | MR

[15] Farina A., On the Classification of Solutions of the Lane-Emden Equation on Unbounded Domains of R N , 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] Gidas B., Spruck J., Global and Local Behavior of Positive Solutions of Nonlinear Elliptic Equations, Comm. Pure Appl. Math. 34 (4) (1981) 525-598. | MR | Zbl

[18] Gidas B., Spruck J., Global a Priori Bounds for Positive Solutions of Nonlinear Elliptic Equations, Comm. Partial Differential Equations 6 (8) (1981) 883-901. | MR | Zbl

[19] Joseph D. D., Lundgren T. S., Quasilinear Dirichlet Problems Driven by Positive Sources, Arch. Rational Mech. Anal. 49 (1-2) (1972/73) 241-269. | MR | Zbl

[20] Murthy M. K.V., Stampacchia G., Boundary Value Problems for Some Degenerate-Elliptic Operators, Ann. Mat. Pura Appl. (4) 80 (1968) 1-122. | MR | Zbl

[21] Lieberman G. M., Boundary Regularity for Solutions of Degenerate Elliptic Equations, Nonlinear Anal. 12 (11) (1988) 1203-1219. | MR | Zbl

[22] Pohozaev S. I., On the Eigenfunctions of the Equation Δu+λfu=0, Dokl. Akad. Nauk SSSR 165 (1965) 36-39. | MR | Zbl

[23] Pucci P., Serrin J., A General Variational Identity, Indiana Univ. Math. J. 35 (3) (1986) 681-703. | MR | Zbl

[24] Pucci P., Serrin J., The Strong Maximum Principle Revisited, J. Differential Equations 196 (1) (2004) 1-66. | MR | Zbl

[25] Serrin J., Local Behavior of Solutions of Quasi-Linear Elliptic Equations, Acta Math. 111 (1964) 247-302. | MR | Zbl

[26] Serrin J., Zou H., Cauchy-Liouville and Universal Boundedness Theorems for Quasilinear Elliptic Equations and Inequalities, Acta Math. 189 (2002). | MR | Zbl

[27] Tolksdorf P., Regularity for a More General Class of Quasilinear Elliptic Equations, J. Differential Equations 51 (1984) 126-150. | MR | Zbl

[28] Vazquez J. L., A Strong Maximum Principle for Some Quasilinear Elliptic Equations, Appl. Math. Optim. (1984) 191-202. | MR | Zbl

Cited by Sources: