Discrete Gronwall inequalities in many variables
نویسندگان
چکیده
منابع مشابه
Generalized Gronwall-Bellman-type discrete inequalities and their applications
* Correspondence: [email protected] School of Science, Shandong University of Technology, Zibo, 255049 Shandong, China Full list of author information is available at the end of the article Abstract In this paper, some new nonlinear Gronwall-Bellman-type discrete inequalities are established, which can be used as a handy tool in the research of qualitative and quantitative properties of solutions ...
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In this paper, we present some new GronwallBellmann type discrete fractional sum inequalities, and based on them present some Volterra-Fredholm type discrete inequalities. These inequalities are of new forms compared with the existing results in the literature, and can be used in the research of boundedness and continuous dependence on the initial value for solutions of fractional difference eq...
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*Correspondence: [email protected] School of Science, Shandong University of Technology, Zhangzhou Road 12, Zibo, Shandong 255049, China Abstract In this paper, some new Gronwall-Bellman-type integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of qualitative and quantitative properties of solutions of dynamic equation...
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As indicated by Pachpatte [15], this result has been frequently used by authors to obtain global existence, uniqueness and stability of solutions of various nonlinear integral and differential equations. On the other hand, Theorem 1.1 has also been extended and generalized by many authors; see, for example, the reference [2, 3, 6, 7, 8, 9, 13, 14, 15, 17, 18]. Like Gronwall type inequalities, (...
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Discrete inequalities, in particular the discrete analogues of the Gronwall–Bellman inequality, have been extensively used in the analysis of finite difference equations. The aim of the present paper is to establish some fractional difference inequalities of Gronwall–Bellman type which provide explicit bounds for the solutions of fractional difference equations.
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1999
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(99)00169-8