Geodesic
Opial's type inequalities on time scales and some applications
S. H. Saker1
1 College of Science Research Centre King Saud University P.O. Box 2455 Riyadh 11451, Saudi Arabia
Annales Polonici Mathematici, Tome 104 (2012) no. 3, pp. 243-260

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap104-3-3
Keywords: prove opial type inequalities time scales employ prove several results related spacing between consecutive zeros solution between zero solution zero its derivative second order dynamic equations time scales apply these inequalities obtain lower bound smallest eigenvalue sturm liouville eigenvalue problem time scales results contain special cases results obtained second order differential equations results difference equations yield conditions disfocality second order dynamic equations time scales

S. H. Saker 1

1 College of Science Research Centre King Saud University P.O. Box 2455 Riyadh 11451, Saudi Arabia 
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S. H. Saker. Opial's type inequalities on time scales and some applications. Annales Polonici Mathematici, Tome 104 (2012) no. 3, pp. 243-260. doi: 10.4064/ap104-3-3

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