A generalization of Opial's inequality and applications to second-order dynamic equations

DOI10.1007/s12591-010-0001-2zbMath1210.34135OpenAlexW2051777633MaRDI QIDQ609429

Özkan Öcalan, Başak Karpuz, Billur Kaymakçalan

Publication date: 30 November 2010

Published in: Differential Equations and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12591-010-0001-2

zbMATH Keywords

time scaledisconjugacydisfocalopial inequalitysecond order dynamic equations

Mathematics Subject Classification ID

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Differential inequalities involving functions of a single real variable (34A40) Dynamic equations on time scales or measure chains (34N05)

Related Items (13)

Some new dynamic Opial type inequalities and applications for second order integro-differential dynamic equations on time scales ⋮ Some inequalities for partial derivatives on time scales ⋮ Some new Opial type dynamic inequalities via convex functions and applications ⋮ Opial and Pólya type inequalities via convexity ⋮ Weighted dynamic inequalities of Opial-type on time scales ⋮ Some new inequalities of Opial's type on time scales ⋮ New inequalities of Opial's type on time scales and some of their applications ⋮ Nonoscillation and oscillation of second-order linear dynamic equations via the sequence of functions technique ⋮ Higher dimensions opial diamond-alpha inequalities on time scales ⋮ Some Opial-type inequalities on time scales ⋮ Some Opial dynamic inequalities involving higher order derivatives on time scales ⋮ Some Opial-type inequalities with higher order delta derivatives on time scales ⋮ Unnamed Item

Cites Work

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• Positive solutions of boundary-value problems for disfocal ordinary differential equations
• On a disconjugacy criterion for second-order dynamic equations on time scales
• Extensions of Pi Opial's inequality
• Opial inequalities on time scales
• Some generalizations for Opial's inequality involving several functions and their derivatives of arbitrary order on arbitrary time scales
• Opial’s inequality and oscillation of 2nd order equations
• Sur une inégalité
• Disconjugate Linear Differential Operators

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