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Sturm theorems for second order linear nonhomogeneous differential equations and localization of zeros of the solution. (English) Zbl 1274.34097

Summary: It is shown that Sturm theorems, formulated in the 1830s and valid for second order linear homogeneous differential equations \(L(y) \equiv y^{\prime\prime}+a(x)y^\prime +b(x)y=0\), could as well be formulated for the class of nonhomogeneous linear differential equations \(L(y)=f(x)\). Criteria for the existence of oscillatory solutions of nonhomogeneous equations as well as more exact locations of the zeros are given.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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