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Stable weak solutions of weighted nonlinear elliptic equations

โœ Scribed by Huang, Xia


Book ID
125838793
Publisher
American Institute of Mathematical Sciences
Year
2014
Tongue
English
Weight
401 KB
Volume
13
Category
Article
ISSN
1534-0392

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โœ Roberta Filippucci; Patrizia Pucci; Marco Rigoli ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 804 KB

In this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of class W possibly singular weights. In order to get the results a new Omori-Yau type principle is used. We complement our nonexistence results by establishing existence of infinitely m

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Given 0 any open and bounded subset of R n , n 4, with smooth boundary and given 7 any (n&m)-dimensional compact submanifold of 0 without boundary, n>m>2, we prove the existence of weak solutions to the problem &2u=u p in 0 { u>0 in 0 u=0 on 0, which are singular on 7, when p is a real p>mร‚(m&2), c