A New Nonlinear Retarded Integral Inequality and Its Application
© Wu-Sheng Wang et al. 2010
Received: 28 April 2010
Accepted: 15 August 2010
Published: 18 August 2010
The main objective of this paper is to establish a new retarded nonlinear integral inequality with two variables, which provide explicit bound on unknown function. This inequality given here can be used as tool in the study of integral equations.
(1.7) was studied by Gripenberg in .
However, the bound given on such inequality in  is not directly applicable in the study of certain retarded differential and integral equations. It is desirable to establish new inequalities of the above type, which can be used more effectively in the study of certain classes of retarded differential and integral equations.
We will prove importance of (1.8) in achieving a desired goal.
2. Main Result
where is a strictly increasing function with and as , is a given positive constant, are bounded functions and nondecreasing in each variable, functions and satisfy hypothesis , i=1,2, and is nondecreasing on such that for .
The authors are very grateful to the editor and the referees for their helpful comments and valuable suggestions. This paper is supported by the Natural Science Foundation of Guangxi Autonomous Region (0991265), the Scientific Research Foundation of the Education Department of Guangxi Autonomous Region (200707MS112), and the Key Discipline of Applied Mathematics of Hechi University of China (200725).
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