Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXXIX, No. 29, pp. 25–60 (2004) 

Selfadjoint differential equations and generalized Karamata functionsJ. Jaros and T. KusanoDepartment of Mathematical Analysis, Faculty of Mathematics, Physics and Informatics, Comenius University, 842 15 Bratislava, SlovakiaDepartment of Applied Mathematics, Faculty of Science, Fukuoka University, 8191 Nanakuma, Jonanku, Fukuoka, 8140180 Japan Abstract: Howard and Maric have recently developed nice nonoscillation theorems for the differential equation $$y^{\prime\prime}+ q(t)y= 0 \eqno (\ast)$$ 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 $$(p(t)y^{\prime})^{\prime}+ q(t)y= 0 \eqno (\ast\ast)$$ 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: selfadjoint differential equation; Karamata functions; generalized Karamata functions; asymptotic behavior Classification (MSC2000): 34C11; 26A12 Full text of the article: (for faster download, first choose a mirror)
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