Improvements of Dynamic Opial-Type Inequalities and Applications
In this paper, we present some new improvements of dynamic Opial-type inequalities of first and higher order on time scales. We employ the new inequalities to prove several results related to the spacing between consecutive zeros of a solution and/or a zero of its derivative of a second-order dynamic equation with a damping term. The main results are proved by making use of a recently introduced new technique for Opial dynamic inequalities, the time scales integration by parts formula, the time scales chain rule, the time scales Taylor formula, and classical as well as time scales versions of Hölder's inequality.
M. Bohner et al., "Improvements of Dynamic Opial-Type Inequalities and Applications," Dynamic Systems and Applications, vol. 24, no. 1-2, pp. 229-241, Dynamic Publishers, Jan 2015.
Mathematics and Statistics
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2015