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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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