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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