## A general construction of linear differential equations with solutions of prescribed properties.(English)Zbl 1054.34018

Summary: Effective constructions of ordinary linear differential equations of arbitrary order are presented that give equations with solutions of prescribed qualitative properties, like solutions in the classes $$L^p$$, converging to zero or bounded solutions, etc. Connections with transformations of equations and distribution of the zeros of solutions are considered as well. Results generalize those obtained for the second-order linear differential equations.

### MSC:

 34A55 Inverse problems involving ordinary differential equations
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### References:

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