Uniqueness of positive solutions of \(\Delta u + u + u^ p = 0\) in a ball. (English) Zbl 0782.35025

Zhang, Liqun

Commun. Partial Differ. Equations 17, No. 7-8, 1141-1164 (1992).

The author proves the uniqueness of positive solutions of the equation \(\Delta u+u+u^ p=0\) on the ball \(B_ r\subset \mathbb{R}^ n\) satisfying the boundary condition \(u=0\) on \(\partial B_ r\) for every \(p\in(1,{{n+2} \over {n-2}}\rangle\), where \(n>2\).

Reviewer: M.Kopáčková (Praha)

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
35B05	Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35J60	Nonlinear elliptic equations

Keywords:

positive solution; radial solution; uniqueness; semilinear elliptic equation