Opial's type inequalities on time scales and some applications

• Autorzy: S. H. Saker
• Języki publikacji: EN

Abstrakty

EN

We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential equations, give some new results for difference equations and yield conditions for disfocality for second order dynamic equations on time scales.

Kategorie tematyczne

• 26D15: Inequalities for sums, series and integrals
• 34K11: Oscillation theory
• 34C10: Oscillation theory, zeros, disconjugacy and comparison theory
• 34A40: Differential inequalities
• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
• 39A13: Difference equations, scaling ( q -differences)
• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2012
• Tom: 104
• Numer: 3
• Strony: 243-260

Daty

wydano

2012

Twórcy

autor

S. H. Saker

• College of Science Research Centre, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Identyfikatory

DOI

10.4064/ap104-3-3