On a weighted Lane–Emden system

References

• Busca J, Manasevich R. A Liouville-type theorem for Lane–Emden systems. Indiana U Math J. 2002;51:37–52.
   Web of Science ®Google Scholar
• Marta G, Manasevich R, Enzo M, Cecilia Y. Existence and nonexistence of positive singular solutions for a class of semilinear elliptic systems. Arch Ration Mech Anal. 1997;140:253–284. doi: 10.1007/s002050050066
   Web of Science ®Google Scholar
• Serrin J, Zou H. Non-existence of positive solutions of Lane–Emden system. Differ Integral Equ. 1996;9:635–653.
   Google Scholar
• Serrin J, Zou H. Existence of positive solutions of Lane–Emden system. Atti Sem Mat Fis Univ Modena. 1998;46:369–380.
   Google Scholar
• Souplet P. The proof of the Lane–Emden conjecture in four space dimensions. Adv Math. 2009;221:1409–1427. doi: 10.1016/j.aim.2009.02.014
   Web of Science ®Google Scholar
• Mitidieri E. A Rellich type identity and applications. Comm Partial Differential Equations. 1993;18:125–151. doi: 10.1080/03605309308820923
   Web of Science ®Google Scholar
• Kang DS, Peng SJ. Infinitely many solutions to elliptic systems with critical exponents and Hardy potentials. Sci China Math. 2012;55:2027–2044. doi: 10.1007/s11425-012-4482-z
   Web of Science ®Google Scholar
• Kang DS, Peng SJ. Existence and asymptotic properties of solutions to elliptic systems involving multiple critical exponents. Sci China Math. 2011;54:243–256. doi: 10.1007/s11425-010-4131-3
   Web of Science ®Google Scholar
• Mazzeo R, Pacard F. A construction of singular solutions for a semilinear elliptic equation using asymptotic analysis. J Differ Geom. 1996;44:331–370. doi: 10.4310/jdg/1214458975
   Web of Science ®Google Scholar
• Wang C, Ye D. Some Liouville theorems for Hénon type elliptic equations. J Funct Anal. 2012;262:1705–1727. doi: 10.1016/j.jfa.2011.11.017
   Web of Science ®Google Scholar
• Aronson DG, Serrin J. Local behavior of solutions of quasilinear equations. Arch Ration Mech Anal. 1964;111:247–302.
   Google Scholar
• Serrin J. Isolated singularities of solutions of quasilinear equations. Acta Math. 1965;113:219–240. doi: 10.1007/BF02391778
   Google Scholar
• Deng YB, Li Y, Yang F. On the positive radial solutions of a class of singular semilinear elliptic equations. J Differ Equ. 2012;253:481–501. doi: 10.1016/j.jde.2012.02.017
   Web of Science ®Google Scholar
• Guo ZM, Guan XH, Wan FS. Sobolev type embedding and weak solutions with a prescribed singular set. Sci China Math. 2016;50:1975–1994. doi: 10.1007/s11425-015-0698-0
   Web of Science ®Google Scholar
• Bidaut-Veron MF, Veron L. Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations. Invent Math. 1991;106:489–539. doi: 10.1007/BF01243922
   Web of Science ®Google Scholar
• Dàvila J, del Pino M, Musso M, Wei J. Standing waves for supercritical nonlinear Schrödinger equations. J Differ Equ. 2007;236:164–198. doi: 10.1016/j.jde.2007.01.016
   Web of Science ®Google Scholar
• Ruiz D, Willem M. Elliptic problems with critical exponents and Hardy potentials. J Differ Equ. 2003;190:524–538. doi: 10.1016/S0022-0396(02)00178-X
   Web of Science ®Google Scholar
• Smets D. Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities. Trans Amer Math Soc. 2005;357:2909–2938. doi: 10.1090/S0002-9947-04-03769-9
   Web of Science ®Google Scholar
• Dautray R, Lions JL. Mathematical analysis and numerical methods for science and technology, Vol. 1: physical origins and classical methods. Berlin: Springer-Verlag; 1985.
   Google Scholar
• Guo ZM, Mei LF, Wan FS, Guan XH. Embedding of weighted Sobolev spaces and degenerate elliptic problems. Sci China Math. 2017;60:1399–1418. doi: 10.1007/s11425-016-0403-6
   Web of Science ®Google Scholar
• Dancer EN, Du YH, Guo ZM. Finite Morse index solutions of an elliptic equation with supercritical exponent. J Differ Equ. 2011;250:3281–3310. doi: 10.1016/j.jde.2011.02.005
   Web of Science ®Google Scholar
• Du YH, Guo ZM. Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations. Adv Differ Equ. 2013;18:737–768.
   Web of Science ®Google Scholar
• Du YH, Guo ZM. Finite Morse index solutions of weighted elliptic equations and the critical exponents. Calc Var Partial Differ. 2015;54:3161–3181. doi: 10.1007/s00526-015-0897-z
   Web of Science ®Google Scholar
• Guo ZM, Zhou F. Sub-harmonicity, monotonicity formula and finite Morse index solutions of an elliptic equation with negative exponent. Sci China Math. 2015;58:2301–2316. doi: 10.1007/s11425-015-4988-2
   Web of Science ®Google Scholar