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2013 A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables
Yong Yan
J. Appl. Math. 2013: 1-10 (2013). DOI: 10.1155/2013/853476


This paper deals with a generalized form of nonlinear retarded Gronwall-Bellman type integral inequality in which the maximum of the unknown function of two variables is involved. This form includes both a nonconstant term outside the integrals and more than one distinct nonlinear integrals. Requiring neither monotonicity nor separability of given functions, we apply a technique of monotonization to estimate the unknown function. Our result can be used to weaken conditions for some known results. We apply our result to a boundary value problem of a partial differential equation with maxima for uniqueness.


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Yong Yan. "A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables." J. Appl. Math. 2013 1 - 10, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.34027
MathSciNet: MR3035174
Digital Object Identifier: 10.1155/2013/853476

Rights: Copyright © 2013 Hindawi


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