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On a nonlinear ordinary differential equation. (English) Zbl 0685.34038

This paper analyses the existence and uniqueness of the positive solutions for the nonlinear ordinary differential equation \((K(u)u')'=f(x)u'.\) The main motivation for this study is related to the Boussinesq equation and to the search of solutions with certain supplementary properties. The approach of the author is based on the equivalence of the given equation with an integral equation and on the use of a fixed point argument.
Reviewer: D.Tiba

MSC:

34C11 Growth and boundedness of solutions to ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
45G10 Other nonlinear integral equations
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