Applications of Opial inequalities on time scales on dynamic equations with damping terms

作者：Saker S H^*

来源：Mathematical and Computer Modelling, 2013, 58(11-12): 1777-1790.

DOI：10.1016/j.mcm.2013.04.006

• Opial%26apos
• s inequality
• Disfocality
• Disconjugacy
• Oscillation
• Dynamic equations
• Time scales

In this paper, we will employ some dynamic inequalities of Opial%26apos;s type on time scales to prove several results related to the spacing between consecutive zeros of a solution of a second order dynamic equation with a damping term. We also obtain several results related to the spacing between a zero of the solution and/or a zero of its derivative. As a special case, we will establish some new results for differential and difference equations with damping terms. For illustration, we will derive some well-known results obtained for differential equations without damping terms. The results yield conditions for disfocality and disconjugacy for dynamic equations with damping terms on time scales.

• 出版日期2013-12