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

 

Positive solutions of $ \Delta u+K(x)u\sp p=0$ without decay conditions on $ K(x)$


Author: Xing Bin Pan
Journal: Proc. Amer. Math. Soc. 115 (1992), 699-710
MSC: Primary 35B05; Secondary 35J60
MathSciNet review: 1081700
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Abstract: This paper deals with the existence of positive solutions of the nonlinear elliptic equation $ \Delta u + K(x){u^p} = 0$ in $ {R^n}$ with $ n \geq 3$ and $ \tfrac{n}{{n - 2}} < p < \tfrac{{n + 2}}{{n - 2}}$, where $ K(x)$ does not decay at $ \infty $. The existence of classical positive solutions and singular positive solutions is proved under the hypothesis that $ K$ is radial symmetric, $ K(r) = 1 + H(r)$ is a perturbation of the constant 1, and $ H(r)$ satisfies some conditions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1081700-5
PII: S 0002-9939(1992)1081700-5
Keywords: Semilinear elliptic equation, positive solution, singular solution
Article copyright: © Copyright 1992 American Mathematical Society