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Singular boundary value problems on a half-line. (English) Zbl 0852.34019
The authors consider singular boundary value problems (BVP) of nonlinear second-order differential equations (1) $x''= f(t, x, x')$, (2) $x(0)= r$, $x(\infty)= \text{const}$, (3) $x(0)= r$, $x'(\infty)= \ell$. In (2) the limit $x(\infty)$ is a constant not previously given, but in (3) $\ell$ is a given constant. The main methods used in the article are upper and lower solution techniques. Necessary and sufficient conditions for the existence of a solution to a class of sublinear singular boundary value problems are obtained. As an application the authors consider a singular BVP that arises in nonlinear mechanics.

34B15Nonlinear boundary value problems for ODE
35J25Second order elliptic equations, boundary value problems
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