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

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Self-adjoint differential equations and generalized Karamata functions

J. Jaros and T. Kusano

Department of Mathematical Analysis, Faculty of Mathematics, Physics and Informatics, Comenius University, 842 15 Bratislava, Slovakia
Department of Applied Mathematics, Faculty of Science, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka, 814-0180 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: self-adjoint differential equation; Karamata functions; generalized Karamata functions; asymptotic behavior

Classification (MSC2000): 34C11; 26A12

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Electronic fulltext finalized on: 6 Oct 2003. This page was last modified: 20 Jun 2011.

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