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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the elliptic equation $ D\sb i[a\sb {ij}(x)D\sb jU]-k(x)U+K(x)U\sp p=0$


Author: Fang-Hua Lin
Journal: Proc. Amer. Math. Soc. 95 (1985), 219-226
MSC: Primary 35J60; Secondary 35B05
MathSciNet review: 801327
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Abstract: The problem of the existence and nonexistence of entire, positive solutions to the uniformly elliptic, semilinear equation $ {D_i}[{a_{ij}}(x){D_j}U] - k(x)U + K(x){U^p} = 0$ in $ {{\mathbf{R}}^n}$, where $ p > 1$, is studied. A limiting case when $ K(x)$ is negative and has quadratic decay at infinity is also treated.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0801327-3
PII: S 0002-9939(1985)0801327-3
Article copyright: © Copyright 1985 American Mathematical Society