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.


34B15 Nonlinear boundary value problems for ordinary differential equations
35J25 Boundary value problems for second-order elliptic equations
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