A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables
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. Requiri...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/853476 |
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| _version_ | 1832545878915678208 |
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| author | Yong Yan |
| author_facet | Yong Yan |
| author_sort | Yong Yan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c6380d618ec24185b9a258286c1daaf4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c6380d618ec24185b9a258286c1daaf42025-02-03T07:24:30ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/853476853476A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two VariablesYong Yan0Department of Mathematics, Sichuan University for Nationalities, Kangding, Sichuan 626001, ChinaThis 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.http://dx.doi.org/10.1155/2013/853476 |
| spellingShingle | Yong Yan A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables Journal of Applied Mathematics |
| title | A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables |
| title_full | A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables |
| title_fullStr | A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables |
| title_full_unstemmed | A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables |
| title_short | A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables |
| title_sort | generalized nonlinear gronwall bellman inequality with maxima in two variables |
| url | http://dx.doi.org/10.1155/2013/853476 |
| work_keys_str_mv | AT yongyan ageneralizednonlineargronwallbellmaninequalitywithmaximaintwovariables AT yongyan generalizednonlineargronwallbellmaninequalitywithmaximaintwovariables |