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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()=const, (3) x(0)=r, x ' ()=. In (2) the limit x() is a constant not previously given, but in (3) 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.


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