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Zbl 0685.34017
Gatica, J.A.; Oliker, Vladimir; Waltman, Paul
Singular nonlinear boundary value problems for second-order ordinary differential equations. (English)
[J] J. Differ. Equations 79, No.1, 62-78 (1989). ISSN 0022-0396

The authors study the boundary value problem $(1)\quad y''+f(x,y)=0,$ $\alpha y(0)-\beta y'(0)=0,$ $\gamma y(1)+\delta y'(1)=0,$ where f: (0,1)$\times (0,\infty)\to (0,\infty)$ is continuous and decreasing in y for each fixed x and integrable on [0,1] for each fixed y, $\lim\sb{y\to 0\sp+}f(x,y)=\infty$ uniformly on compact subsets of (0,1). They establish an existence theorem for the problem (1) and state conditions under which the problem (1) has at most one positive solution. The technical arguments involve properties of solutions and the use of iterative techniques. A new fixed point theorem for cones, for decreasing mappings, is developed and used in proofs.
[J.Ohriska]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE

Keywords: iterative techniques

Cited in: Zbl 1174.34327 Zbl 1173.34015 Zbl 1069.34012 Zbl 0953.34014 Zbl 0861.39002 Zbl 0816.34046 Zbl 0731.34015

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