Differential and Integral Equations

Uniqueness of positive radial solutions of $\Delta u+f(\vert x\vert ,u)=0$

Lynn Erbe and Moxun Tang

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We study the uniqueness of positive radial solutions to the Dirichlet boundary value problem for the semilinear elliptic equation $\Delta u+f(|x|,u)=0$ in a finite ball or annulus in $R^n$, $n\ge 3$. Applying our main results to the cases when $f$ is independent of $t$, or $f$ is of the form $K(t)u^p$, we can establish some earlier known results and obtain some new results in an easier and unified approach.

Article information

Differential Integral Equations, Volume 11, Number 5 (1998), 725-743.

First available in Project Euclid: 30 April 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Erbe, Lynn; Tang, Moxun. Uniqueness of positive radial solutions of $\Delta u+f(\vert x\vert ,u)=0$. Differential Integral Equations 11 (1998), no. 5, 725--743. https://projecteuclid.org/euclid.die/1367329667

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