A Generalized Nonlinear Gronwall‐Bellman Inequality with Maxima in Two Variables

Yong Yan

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/853476

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:853476

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