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Biles, Daniel C.; Robinson, Mark P.; Spraker, John S.

A generalization of the Lane-Emden equation. (English) Zbl 1035.34003

J. Math. Anal. Appl. 273, No. 2, 654-666 (2002).
The authors study the initial value problem \(y''(t)+p(t)y'(t)+q(t,y(t))=0\), \(y(0)=a\), \(y'(0)=0\). Four conditions on \(p\) and \(q\) are established so that a solution to the initial value problem exists. If additionally \(q\) is Lipschitzian then the solution is unique.
Reviewer: Dana Petcu (Timişoara)

Cited in 12 Documents

MSC:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L05 Numerical methods for initial value problems involving ordinary differential equations

Keywords:

second-order initial value problems; solution existence; solution uniqueness
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\textit{D. C. Biles} et al., J. Math. Anal. Appl. 273, No. 2, 654--666 (2002; Zbl 1035.34003)
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References:

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