## Differential and Integral Equations

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

### A uniqueness result for certain semilinear elliptic equations

#### 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