A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables | Zendy

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

Author(s) -

Yong Yan

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/853476

Subject(s) - mathematics , uniqueness , monotonic function , nonlinear system , gronwall's inequality , maxima , function (biology) , mathematical analysis , boundary value problem , term (time) , inequality , art , physics , quantum mechanics , evolutionary biology , performance art , biology , art history

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 nonconstantterm 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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