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The existence of positive entire solutions about singular nonlinear elliptic equations. (Chinese. English summary) Zbl 0848.35038
Summary: The goal of this paper is to study the following nonlinear equation: \[ \Delta u= f(|x|, u, |\nabla u|) u^{- \lambda},\quad x\in \mathbb{R}^2,\quad 0< \lambda< 1.\tag{1} \] The author gives a theorem of the existence of positive entire solutions of (1) and discusses the properties of the solutions at infinity.

MSC:
35J60 Nonlinear elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
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