含多个非线性项的时滞积分不等式及其应用  

Retarded Integral Inequality With Multiple Nonlinear Terms and Its Application

作　　者：王五生[1,2] 李自尊[1,3] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,桂林广西541004 [2]河池学院数学系,宜州广西546300 [3]百色学院数学与计算机信息工程系,百色广西533000

出　　处：《数学进展》2012年第5期597-604,共8页Advances in Mathematics（China）

基　　金：国家自然科学基金项目(No.11161018);广西自然科学基金项目(No.2012GXNSFAA053009;No.0991265);广西教育厅科学研究项目(No.200707MSll2)

摘　　要：本文在文献[Agarwal et al.,J.Inequ.Appl,2008,Art.ID 908784,15 pages]和文献[Chen et al.,J.Inequ.Appl.,2009,Art.ID 258569,15 pages]的基础上,建立了一类新的非线性时滞积分不等式。第一个参考文献中不等式的未知函数u是一元函数,右端第一项是正常数c;第二个参考文献中不等式右端第一项也是正常数c,第二项的被积函数中只含未知函数线性因子;本文研究的不等式中未知函数是二元函数,右端第一项是不减的正函数,第二项被积函数中含有未知函数的非线性因子,积分号外还有一个非常数因子.最后,本文用研究不等式得到的结果讨论了时滞偏微分方程初边值问题的有界性.On the basis of [Agarwal et al., J. Inequ. Appl., 2008, Art. ID 908784, 15 pages] and [Chen et al., J. Inequ. Appl., 2009, Art. ID 258569, 15 pages], this paper establishes a new nonlinear retarded integral inequality. In the first literature the unknown function u of the inequality is a single variable function, the first term of the right hand of the inequality is positive constant c; in the second literature the first term of the right hand of the inequality is also a positive constant, and the integrand of the second term only contains linear factors of unknown function. In this paper, the unknown function of the inequality is a two-variable function, the first term of the right hand of the inequality is a nondecreasing and positive function, and the integrand of the second term contains a nonlinear factor of unknown function, and it also contains a nonconstant factor outside the integral sign. Finally, We apply our result to the discussion of boundedness for the initial-boundary value problem of retarded partial differential equation.

关 键 词：积分不等式 时滞 解的估计 边值问题 

分 类 号：O178[理学—数学]