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

Advances in Difference Equations

Ravi P Agarwal¹  Xun-Huan Deng³  Qi-Ru Wang³ 

[1] Department of Mathematics, Texas A&M University-Kingsville, Kingsville, USA;School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, P.R. China

关键词: neutral dynamic equations;    positive and negative coefficients;    oscillation and nonoscillation;    lower and upper solutions;    Kranoselskii’s fixed point theorem;   

DOI  :  10.1186/1687-1847-2014-115

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY