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Zbl 0852.34019
Chen, Shaozhu; Zhang, Yong
Singular boundary value problems on a half-line. (English)
[J] J. Math. Anal. Appl. 195, No.2, 449-468 (1995). ISSN 0022-247X

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.\par 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.
[A.I.Kolosov (Khar'kov)]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
35J25 Second order elliptic equations, boundary value problems

Keywords: singular boundary value problems; nonlinear second-order differential equations

Cited in: Zbl 1114.34019

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Zentralblatt MATH Berlin [Germany]