References
- Liouville J. C. R. Acad. Sci. Paris. 1844;19:1262.
- Cauchy A. Mémoires sur les fonctions complémentaires [Memoirs on complementary functions]. C. R. Acad. Sci. Paris. 1844;19:1377–1384.
- Gidas B, Spruck J. Global and local behavior of positive solutions of nonlinear elliptic equations. Commun. Pure Appl. Math. 1981;34:525–598.
- Gidas B, Spruck J. A priori bounds for positive solutions of a nonlinear elliptic equations. Commun. Partial Differ. Equ. 1981;6:883–901.
- Chen WX, Li C. Classification of solutions of some nonlinear elliptic equations. Duke Math. J. 1991;63:615–622.
- Gidas B. Symmetry properties and isolated singularities of positive solutions of nonlinear elliptic equations. In: Nonlinear partial differential equations in engineering and applied science (Proc. Conf., Univ. Rhode Island, Kingston, R.I., 1979). Vol. 54, Lecture notes in pure and applied mathematics. New York (NY): Dekker; 1980. p. 255–273.
- Berestycki H, Dolcetta IC, Nirenberg L. Superlinear indefinite elliptic problems and nonlinear Liouville theorems. Topol. Methods Nonlinear Anal. 1994;4:59–78.
- Poláčik P, Quittner P, Souplet P. Singularity and decay estimates in superlinear problems via Liouville-type theorems, I: elliptic equations and systems. Duke Math. J. 2007;139:555–579.
- Quittner P, Souplet P. Superlinear parablolic problems: blow-up, global existence and steady states. Basel: Birkhäuser Verlag; 2007.
- Serrin J, Zou H. Cauchy--Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities. Acta Math. 2002;189:79–142.
- Cuccu F, Mohammed A, Porru G. Extensions of a theorem of Cauchy--Liouville. J. Math. Anal. Appl. 2010;369:222–231.
- Kogoj AE, Lanconelli E. Liouville theorems in halfspaces for parabolic hypoelliptic equations. Ric. Mat. 2006;55:267–282.
- Kogoj AE, Lanconelli E. Liouville theorem for X-elliptic operators. Nonlinear Anal. 2009;70:2974–2985.
- Dolcetta IC, Cutrì A. On the Liouville property for the sublaplacians. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 1997;25:239–256.
- D’Ambrosio L, Lucente S. Nonlinear Liouville theorems for Grushin and Tricomi operators. J. Differ. Equ. 2003;193:511–541.
- Monti R, Morbidelli D. Kelvin transform for Grushin operators and critical semilinear equations. Duke Math. J. 2006;131:167–202.
- Monticelli DD. Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators. J. Eur. Math. Soc. 2010;12:611–654.
- Yu X. Liouville type theorem for nonlinear elliptic equation involving Grushin operators. Commun. Contem. Math. 2015;17:1450050 (12p).
- Filippucci R, Pucci P, Rigoli M. Non-existence of entire solutions of degenerate elliptic inequalities with weights. Arch. Ration. Mech. Anal. 2008;188:155–179.
- Serrin J, Zou H. Non-existence of positive solutions of Lane--Emden systems. Differ. Integr. Equ. 1996;9:635–653.
- Souto MAS. A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems. Differ. Integr. Equ. 1995;8:1245–1258.
- Mitidieri E, Pokhozhaev SI. A priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities. Proc. Steklov Inst. Math. 2001;234:1–362.
- Mitidieri E. Nonexistence of positive solutions of semilinear elliptic systems in ℝN. Differ. Integr. Equ. 1996;9:465–479.
- Souplet P. The proof of the Lane--Emden conjecture in four space dimensions. Adv. Math. 2009;221:1409–1427.
- Kogoj AE, Lanconelli E. On semilinear Δλ-Laplace equation. Nonlinear Anal. 2012;75:4637–4649.
- Franchi B, Lanconelli E. Une métrique associée à une classe d’opérateurs elliptiques dégénérés, (French) [A metric associated with a class of degenerate elliptic operators] Conference on linear partial and pseudodifferential operators (Torino, 1982). Rend. Sem. Mat. Univ. Politec. Torino 1983, Special Issue. 1984;1983:105–114.
- Thuy PT, Tri NM. Nontrivial solutions to boundary value problems for semilinear strongly degenerate elliptic differential equations. NoDEA Nonlinear Differ. Equ. Appl. 2012;19:279–298.
- Anh CT, My BK. Existence of solutions to Δλ-Laplace equations without the Ambrosetti--Rabinowitz condition. Complex Var. Elliptic Equ. 2016;61:137–150. doi: 10.1080/17476933.2015.1068762.
- Luyen DT, Tri NM. Existence of solutions to boundary-value problems for semilinear Δγ differential equations. Math. Notes. 2015;97:73–84.