Oscillation and nonoscillation for second order neutral dynamic equations with positive and negative coefficients on time scales

被引：0
作者：
Xun-Huan Deng
Qi-Ru Wang
Ravi P Agarwal
机构：
[1] Sun Yat-Sen University,School of Mathematics and Computational Science
[2] Texas A&M University-Kingsville,Department of Mathematics
[3] King Abdulaziz University,Department of Mathematics
来源：
Advances in Difference Equations | / 2014卷
关键词：
neutral dynamic equations; positive and negative coefficients; oscillation and nonoscillation; lower and upper solutions; Kranoselskii’s fixed point theorem;
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摘要：
We investigate oscillation and nonoscillation of certain second order neutral dynamic equations with positive and negative coefficients. We apply the results from the theory of lower and upper solutions for related dynamic equations along with some additional estimates on positive solutions and use different techniques to obtain some oscillatory theorems. Also, we apply Kranoselskii’s fixed point theorem to obtain nonoscillatory results and then give two sufficient and necessary conditions for the equations to be oscillatory. Some interesting examples are given to illustrate the versatility of our results.
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