Differential and Integral Equations

A uniqueness result for certain semilinear elliptic equations

Michael A. Karls

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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 $q>p>(n+2)/(n-2)$.

Article information

Source
Differential Integral Equations, Volume 9, Number 5 (1996), 949-966.

Dates
First available in Project Euclid: 6 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367871525

Mathematical Reviews number (MathSciNet)
MR1392089

Zentralblatt MATH identifier
0927.35035

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 34B15: Nonlinear boundary value problems 35B05: Oscillation, zeros of solutions, mean value theorems, etc.

Citation

Karls, Michael A. A uniqueness result for certain semilinear elliptic equations. Differential Integral Equations 9 (1996), no. 5, 949--966. https://projecteuclid.org/euclid.die/1367871525


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