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1996 A uniqueness result for certain semilinear elliptic equations
Michael A. Karls
Differential Integral Equations 9(5): 949-966 (1996).

Abstract

For the problem $\Delta u + f(u)=0 \ \text{ in } \ \Bbb R^n$; $u(x)\rightarrow 0, \ \text{as} \ |x| \rightarrow \infty$ we use a shooting method to prove that there is at most one positive radially symmetric solution if $u$ decays like $|x|^{-(n-2)}$ as $|x| \rightarrow \infty$, and $f$ is similar in shape to $f(u)=u^p-u^q$ with $n>2$ and $q>p>(n+2)/(n-2)$.

Citation

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Michael A. Karls. "A uniqueness result for certain semilinear elliptic equations." Differential Integral Equations 9 (5) 949 - 966, 1996.

Information

Published: 1996
First available in Project Euclid: 6 May 2013

zbMATH: 0927.35035
MathSciNet: MR1392089

Subjects:
Primary: 35J60
Secondary: 34B15 , 35B05

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.9 • No. 5 • 1996
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