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Positive solutions of singular elliptic equations outside the unit disk. (English) Zbl 0985.34015

The author deals with existence and asymptotic behaviour of positive solutions to a semilinear elliptic equation \(\Delta u+\varphi(x,u)=0\) outside the unit disc in \(\mathbb{R}^2\) with a homogeneous Dirichlet boundary condition.

MSC:

34B16 Singular nonlinear boundary value problems for ordinary differential equations
35J65 Nonlinear boundary value problems for linear elliptic equations
34B27 Green’s functions for ordinary differential equations
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