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Comparison theorems for second order nonselfadjoint differential systems. (English) Zbl 0532.34025

Comparison theorems are given for second order ordinary differential equations of the form \((r(t)x')'+p(t)x=0\) where r(t), p(t) and the corresponding quantities R(t), P(t) of the comparison equation are continuous nonsingular matrices. No sign restrictions are made on the elements of r and p. In a comparison theorem for conjugate points it is supposed that r(t) and R(t) are diagonal matrices whereas two theorems on focal points do not require this restriction.
Reviewer: B.Aulbach

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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