Differential and Integral Equations

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

Lynn Erbe and Moxun Tang

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We investigate the global structure of positive radial solutions of a semilinear elliptic equation $\Delta u+K(|x|)\gamma (u)=0$, and study the uniqueness of ground state solutions of this equation. Our discussion is based on a Pohozaev-type identity and some detailed investigation for the oscillatory and asymptotic behavior of the solutions and their variational functions.

Article information

Differential Integral Equations, Volume 11, Number 4 (1998), 663-678.

First available in Project Euclid: 30 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 35B05: Oscillation, zeros of solutions, mean value theorems, etc.


Erbe, Lynn; Tang, Moxun. Uniqueness of positive radial solutions of $\Delta u+K(\vert x\vert )\gamma(u)=0$. Differential Integral Equations 11 (1998), no. 4, 663--678. https://projecteuclid.org/euclid.die/1367341039

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