Displaying similar documents to “Some dynamic inequalities applicable to partial integrodifferential equations on time scales”

Nabla inequalities and permanence for a logistic integrodifferential equation on time scales

Meng Hu, Lili Wang (2017)

Open Mathematics

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In this paper, by using the theory of calculus on time scales and some mathematical methods, several nabla dynamic inequalities on time scales are established. As an application, we apply the obtained results to a logistic integrodifferential equation on time scales and sufficient conditions for the permanence of the equation are derived. Finally, numerical examples together with their simulations are presented to illustrate the feasibility and effectiveness of the results.

Opial inequalities on time scales

Martin Bohner, Bıllûr Kaymakçalan (2001)

Annales Polonici Mathematici

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We present a version of Opial's inequality for time scales and point out some of its applications to so-called dynamic equations. Such dynamic equations contain both differential equations and difference equations as special cases. Various extensions of our inequality are offered as well.

Opial's type inequalities on time scales and some applications

S. H. Saker (2012)

Annales Polonici Mathematici

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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...