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Sturmian theory for a class of nonlinear second-order differential equations. (English) Zbl 0816.34026
The author extends some results for Sturmian theory to the class of nonlinear second-order differential equations satisfying the boundary- value problem \(u_{xx} + f(s(x)u)u =0\), \((x \in (a,b))\), \(u(a) \cos (\alpha) - u_ x(a) \sin (\alpha) = 0\), \(u(b) \cos (\beta) - u_ x(b) \sin (\beta) = 0\) for certain parameters \(\alpha\) and \(\beta\). In the equation \(f\) and \(s\) satisfy certain continuity requirements and \(f(t) > 0\) for \(t \neq 0\), and \(s(x) > 0\) for \(x \geq a\).
Reviewer: P.Smith (Keele)

MSC:
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34B15 Nonlinear boundary value problems for ordinary differential equations
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