## Remarks on the existence of regularly varying solutions for second order linear differential equations.(English)Zbl 1052.34042

By using the fixed-point principle, the authors prove necessary and sufficient conditions for the regularity in the sense of Karamata (implying nonoscillation) of all solutions of the equation $$y''+f(x)y=0$$. The result is is not new, but the method presented here is also suitable for some nonlinear equations.

### MSC:

 34C11 Growth and boundedness of solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations

### Keywords:

fixed-point method
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