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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Positive solutions of $\Delta u+K(x)u^ p=0$ without decay conditions on $K(x)$
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by Xing Bin Pan PDF
Proc. Amer. Math. Soc. 115 (1992), 699-710 Request permission

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
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 115 (1992), 699-710
  • MSC: Primary 35B05; Secondary 35J60
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1081700-5
  • MathSciNet review: 1081700