Asymptotic dichotomy in a class of higher order nonlinear delay differential equations

Journal of Inequalities and Applications

Haihua Liang¹  Yunhua Ye² 

[1] School of Mathematics and Systems Science, Guangdong Polytechnic Normal University;School of Mathematics, Jiaying University;

关键词: Asymptotic behavior;    delay differential equation;    higher order differential equation;    oscillation;    Schwarz inequality;   

DOI  :  10.1186/s13660-018-1949-7

来源: DOAJ

【 摘 要 】

Abstract Employing a generalized Riccati transformation and integral averaging technique, we show that all solutions of the higher order nonlinear delay differential equation y(n+2)(t)+p(t)y(n)(t)+q(t)f(y(g(t)))=0 $$ y^{(n+2)}(t)+p(t)y^{(n)}(t)+q(t)f\bigl(y\bigl(g(t)\bigr)\bigr)=0 $$ will converge to zero or oscillate, under some conditions listed in the theorems of the present paper. Several examples are also given to illustrate the applications of these results.

【 授权许可】

Unknown