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Conjugacy criteria for second order differential equations. (English) Zbl 0794.34025
Oscillation properties of the equation $$(*)$$ $$[r(x)y'(x)]'+ p(x)y(x)= 0$$ on a finite or infinite interval are studied via perturbation of the disconjugate equation $$(**)$$ $$[r(x)y'(x)]'= 0$$. Sufficient conditions, in terms of the coefficients $$r(\cdot)$$, $$p(\cdot)$$, are given so that $$(*)$$ possesses a nontrivial solution with at least two zeros. It is shown that the conjugacy criteria for $$(*)$$ are different when the principal solutions satisfy certain linear dependencies.

##### MSC:
 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A30 Linear ordinary differential equations and systems
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##### References:
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