非线性时滞积分不等式的推广

The Generalization of Nonlinear Integral Inequality with Delay

欧阳型不等式在常微分方程、偏微分方程及差分方程的定性、稳定性理论的研究中是一个强有力的工具.许多学者对欧阳不等式进行了各种形式的推广和改进.文章利用辅助函数法,在已有的非线性时滞积分不等式的基础上添加非常数的系数,且将原来的单变元推广到n个无关变元,建立了带有时滞的关于n个无关变元的欧阳型非线性积分不等式,此结果在本质上推广了已有的相关结果,在研究微分方程定性理论中起着重要作用.

Ou-Yang type inequalities are effective tools in studying qualitative theory and stability theory of ordinary differential equation,partial differential equation and difference equation. Many scholars have gener-alized and improved Ou-Yang type inequalities.In this paper,by using auxiliary function and adding non-constant coefficients to established new inequalities on the basis of some nonlinear integral inequalities ,a new nonlinear integral inequality in n independent variables with retardation and non-constant coefficients is established,which generalizes and improves some existed results,and plays an important role in the qualitative theory of certain differential equations.