Non-existence of positive solutions of semilinear elliptic systems. (English) Zbl 0900.35121

Serrin, James; Zou, Henghui

Bakelman, I. R. (ed.) et al., A tribute to Ilya Bakelman. Proceedings of a conference, College Station, TX, USA, October 1993. College Station, TX: Texas A & M University. Discourses Math. Appl. 3, 55-68 (1994).

The authors prove several nonexistence results for positive solutions with a prescribed growth at infinity of the weakly coupled system \[ \Delta u+ f(v)=0,\quad \Delta v+g(u)=0\quad\text{in }\mathbb{R}^n. \]
For the entire collection see [Zbl 0845.00031].

MSC:

35J60	Nonlinear elliptic equations
35J45	Systems of elliptic equations, general (MSC2000)

Keywords:

nonexistence; weakly coupled system