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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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