Sturmian theory for a class of nonlinear second-order differential equations (Q1340579)

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 \(x \geq a\).