Stable weak solutions of weighted nonlinear elliptic equations | Zendy

Xia Huang | Zendy

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Stable weak solutions of weighted nonlinear elliptic equations

Author(s) -

Xia Huang

Publication year - 2013

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2014.13.293

Subject(s) - nabla symbol , bounded function , omega , domain (mathematical analysis) , nonlinear system , alpha (finance) , physics , type (biology) , elliptic curve , mathematical analysis , combinatorics , mathematics , pure mathematics , quantum mechanics , ecology , construct validity , statistics , biology , psychometrics

This paper deals with the weighted nonlinear elliptic equation -div(|x|?u) = |x|eu in u = 0 on ? where , ? satisfy N + > 2 and - > -2, and the domain ? ?N(N 2) is bounded or not. Moreover, when 0, we prove that, for N + > 2, - -2, the above equation admits no weak solution. We also study Liouville type results for the equation in ?N.

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