Geodesic
Self-adjoint differential equations and generalized Karamata functions
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 29 (2004) no. 1.

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Howard and Marić have recently developed nice nonoscillation theorems for the differential equation $$y^{\prime\prime}+ q(t)y= 0 \eqno{\rm (\ast)}$$ by means of regularly varying functions in the sense of Karamata. The purpose of this paper is to show that their results can be fully generalized to differential equations of the form $$(p(t)y^{\prime})^{\prime}+ q(t)y= 0 \eqno{\rm (\ast\ast)}$$ by using the notion of generalized Karamata functions, which is needed to comprehend how delicately the asymptotic behavior of solutions of ($\ast\ast$) is affected by the function $p(t)$.
Keywords: Self-adjoint differential equation, Karamata functions, generalized Karamata functions, asymptotic behavior 
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     title = {Self-adjoint differential equations and generalized {Karamata} functions},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
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     publisher = {mathdoc},
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J. Jaroš; T. Kusano. Self-adjoint differential equations and generalized Karamata functions. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 29 (2004) no. 1. http://geodesic.mathdoc.fr/item/BASS_2004_29_1_a2/