EXHAUSTIVE EXISTENCE AND NON-EXISTENCE RESULTS FOR HARDY–HÉNON EQUATIONS IN Rn

[BC98] H. BREZIS AND X. CABRE´, Some simple nonlinear PDE’s without solutions, Boll. Unione Mat. Ital. 1-B (1998) 223–262. 2

[BK92] H. BREZIS, S. KAMIN, Sublinear elliptic equations in Rn, Manuscripta Math. 74 (1992) 87–106. 2 [CLi91] W. CHEN AND C. LI, Classification of solutions of some nonlinear elliptic equations. Duke Math. J. 63 (1991), 615-622. 2

[DQ20] W. DAI AND G. QIN, Liouville type theorems for Hardy–He´non equations with concave nonlineari- ties, Math. Nachr. 293 (2020) 1084–1093. 2, 3, 13

[DDG11] E.N. DANCER, Y. DU, AND Z. GUO, Finite Morse index solutions of an elliptic equation with supercritical exponent, J. Differential Equations 250 (2011) 3281–3310. 2, 3

[GS81] B. GIDAS AND J. SPRUCK, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981) 525–598. 2

[Gig86] Y. GIGA, On elliptic equations related to self-similar solutions for nonlinear heat equations. Hi- roshima Math. J. 16 (1986) 539–552. 24, 26

[GG98] M.-H. GIGA AND Y. GIGA, A subdifferential interpretation of crystalline motion under nonuniform driving force. Dynamical systems and differential equations, Vol. I (Springfield, MO, 1996). Discrete Contin. Dynam. Systems 1998, Added Volume I, 276–287. 21

[GT96] R. GE´RARD AND H. TAHARA, Singular nonlinear partial differential equations. Aspects of Mathe- matics. Friedr. Vieweg & Sohn, Braunschweig, 1996. viii+26. 20

[LGZ06] J.Q. LIU, Y. GUO, AND Y.J. ZHANG, Existence of positive entire solutions for polyharmonic equa- tions and systems, J. Partial Differential Equations 19 (2006) 256–270. 2

[MP01] E. MITIDIERI AND S.I. POHOZAEV, A priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities, Tr. Mat. Inst. Steklova 234 (2001) 1–384. 2, 4, 5

[NN†20] Q.A. NGOˆ , V.H. NGUYEN, Q.H. PHAN, AND D. YE, Exhaustive existence and non-existence results for some prototype polyharmonic equations, J. Differential Equations 269 (2020) 11621–11645. 2

[NY20] Q.A. NGOˆ AND D. YE, Existence and non-existence results for the higher order Hardy–He´non equa- tion revisited, arXiv:2007.09652, 2020. 2, 4 n+2

[Ni82] W.M. NI, On the elliptic equation ∆u + K(x)u n−2 = 0, its generalizations, and applications in geometry, Indiana Univ. Math. J. 31 (1982) 493–529. 2, 3

[Ni86] W.M. NI, Uniqueness, nonuniqueness and related questions of nonlinear elliptic and parabolic equa- tions, Nonlinear functional analysis and its applications, Part 2, 229–241, Proc. Sympos. Pure Math., 45, Part 2, Amer. Math. Soc., Providence, RI, 1986. 2, 3

[PS12] Q.H. PHAN AND P. SOUPLET, Liouville-type theorems and bounds of solutions of Hardy–He´non equations, J. Differential Equations 252 (2012) 2544–2562. 4, 5, 18

[Per01] L. PERKO, Differential equations and dynamical systems. Third edition. Texts in Applied Mathemat- ics, 7. Springer-Verlag, New York, 2001. 22, 23, 29

[RZ00] W. REICHEL AND H. ZOU, Non-existence results for semilinear cooperative elliptic systems via moving spheres, J. Differential Equations 161 (2000) 219–243. 2, 3

[SZ96] S. SERRIN AND H. ZOU, Non-existence of positive solutions of Lane-Emden systems, Differential Integral Equations 9 (1996) 635–653. 13

(Y. Giga) GRADUATE SCHOOL OF MATHEMATICAL SCIENCES, THE UNIVERSITY OF TOKYO, 3-8-1 KOMABA, MEGURO-KU, TOKYO 153-8914, JAPAN Email address: labgiga@ms.u-tokyo.ac.jp

(Q.A. Ngoˆ) UNIVERSITY OF SCIENCE, VIETNAM NATIONAL UNIVERSITY, HANOI, VIETNAM Email address: nqanh@vnu.edu.vn