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Existence of solutions for nonlinear singular boundary value problems. (English) Zbl 0666.34017

Existence of solutions to the two-point boundary value problem \((p(t)y')'=q(t)f(t,y,p(t)y'),\) \(y(1)=0\), \(\lim_{t\to 0+}p(t)y'(t)=0\) is established under a variety of conditions. Here \(p(0)=0\) is allowed, and q is not assumed to be continuous at 0, so the problem may be doubly singular. In addition, the Dirichlet problem for this differential equation is investigated.
Reviewer: L.E.Bobisud

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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[1] DOI: 10.1016/0022-247X(88)90376-9 · Zbl 0646.34003
[2] DOI: 10.1080/00036818608839643 · Zbl 0584.34012
[3] DOI: 10.1016/0362-546X(88)90070-3 · Zbl 0653.34015
[4] Chan C.Y., Quart. Appl. Math. 45 pp 591– (1987)
[5] Corduneanu C., Principles of Differential and Integral Equations (1977) · Zbl 0208.10701
[6] DOI: 10.1137/0517044 · Zbl 0595.34016
[7] DOI: 10.1016/0022-247X(86)90003-X · Zbl 0616.34012
[8] Granas A., Nonlinear Boundary Value Problems for Ordinary Differential Equations (1985) · Zbl 0615.34010
[9] Regan D.O., Some new results for second order boundary value problems
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