Results 181 to 190 of about 485,864 (198)

Gronwall Inequalities in Higher Dimensions

1991
Several authors generalized inequalities of Gronwall type to the case of functions of two or more variables. Of course, such results have application in the theory of partial differential equations and Volterra integral equations.
D. S. Mitrinović, J. E. Pečarić, A. M. Fink   +2 more
openaire   +1 more source

An extension of Gronwall's inequality

2020
One of the results in this paper is the extended Gronwall's inequality. Theorem: Let \(k\geq 1\) be an integer. Suppose that \[ \varphi^k(t)\leq c_0^k(t)+ \int_0^t [kc_1(s)+ kc_2(s) \varphi^2(s)+\dots+ kc_k(s) \varphi^k(s)] ds \] for a.e. \(t\in[0,T]\), where \(c_0\geq 0\) is nonincreasing, \(\varphi\in L^\infty\) and \(\varphi\geq 0\) for a.e. \(t\in [
openaire   +2 more sources

A Cousin of Gronwall's Inequality: 11135

The American Mathematical Monthly, 2006
Ray Redheffer, Richard Stong
openaire   +2 more sources

A Generalized Fractional (q, h)–Gronwall Inequality and Its Applications to Nonlinear Fractional Delay (q, h)–Difference Systems

Mathematical Methods in the Applied Sciences, 2021
Baoguo Jia, Feifei Du
exaly  

Some Gronwall–Bellman Inequalities on Time Scales and Their Continuous Forms: A Survey

Symmetry, 2021
Francesca Barich
exaly  

On Some New Integral Inequalities of Gronwall–Bellman–Pachpatte Type

Applied Mathematics and Computation, 2011
A Abdeldaim
exaly  

Discrete Gronwall Inequalities in Many Variables

Computers and Mathematics With Applications, 1999
R P Agarwal
exaly  

Generalized Gronwall Fractional Summation Inequalities and Their Applications

Journal of Inequalities and Applications, 2015
Run Xu
exaly  

A Unified Approach to Continuous and Discrete Gronwall-Bellman Inequalities

Applicable Analysis, 1992
Chung-Lie Wang
exaly  

Weakly Singular Gronwall Inequalities and Applications to Fractional Differential Equations

Journal of Mathematical Analysis and Applications, 2019
J R L Webb
exaly