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On the boundedness of the number of orthogonal solutions of the equation \(-u''+q(x)u=\lambda u\). (Russian) Zbl 0693.34037
Consider the differential equation \(u''+\lambda u=q(x)\) where \(\lambda\) and q are complex valued. Let \(\sqrt{-\lambda}=\rho +i\nu\), with \(\rho\geq 0\) and \(\nu\geq 0\) when \(\rho =0\). For given \(\rho_ 0>0\), if \(| \nu | \leq C_{\rho}\) \((1<C<\infty)\) and \(\rho \geq \rho_ 0\) then there exist at most two pairs of nontrivial solutions orthogonal on the interval (-1,1).
Reviewer: D.Bobrowski

MSC:
34C11 Growth and boundedness of solutions to ordinary differential equations
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