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Fractal oscillations for a class of second order linear differential equations of Euler type. (English) Zbl 1145.34022
s-dimensional fractal oscillations of continuous and smooth functions defined on an open bounded interval are introduced and studied. The author establishes this kind of oscillations for solutions of a class of second order linear differential equations of Euler type. Moreover, it it is shown that the dimensional number s only depends on a positive real parameter α appearing in a singular term of the main equation.
MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A30Linear ODE and systems, general