scholarly journals Nonlinear integral inequality with power and its application in delay integro-differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yazhou Tian ◽  
Min Fan
Keyword(s):  
Differential Equations ◽  
Integral Inequality ◽  
Nonlinear Integral Inequality

scholarly journals Integral inequalities and applications

1980 ◽  
Vol 21 (1) ◽  
pp. 13-20 ◽  
Author(s):  
K. Narsimha Reddy
Keyword(s):  
Differential Equations ◽  
Integral Inequality ◽  
Integral Inequalities

In this paper some nonlinear analogues of Gronwall's integral inequality are established and an application to differential equations is given.

scholarly journals A Nonlinear Weakly Singular Retarded Henry-Gronwall Type Integral Inequality and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yuanhua Lin ◽  
Shanhe Wu ◽  
Wu-Sheng Wang
Keyword(s):  
Differential Equations ◽  
Singular Integral ◽  
Fractional Differential Equations ◽  
Integral Inequality ◽  
Analysis Techniques ◽  
Weakly Singular ◽  
Type Integral ◽  
Explicit Bounds ◽  
Fractional Differential ◽  
Equations With Delay

We establish a class of new nonlinear retarded weakly singular integral inequality. Under several practical assumptions, the inequality is solved by adopting novel analysis techniques, and explicit bounds for the unknown functions are given clearly. An application of our result to the fractional differential equations with delay is shown at the end of the paper.

Upper and Lower Bounds of Unknown Functions in Several Nonlinear Integral Inequalities in Engineering

2014 ◽  
Vol 1008-1009 ◽  
pp. 1517-1520
Author(s):  
Li Mian Zhao ◽  
Ji Ting Huang ◽  
Wu Sheng Wang
Keyword(s):  
Lower Bounds ◽  
Integral Inequality ◽  
Unknown Function ◽  
Integral Inequalities ◽  
Upper And Lower Bounds ◽  
Nonlinear Integral Inequality ◽  
Amplification Method ◽  
Lower Estimation ◽  
Change Of Variable ◽  
Linear Integral

In this paper, we discuss the upper and lower bounds of unknown functions in several nonlinear integral inequalities. Firstly, we give out the upper estimation of unknown function of a nonlinear integral inequality. Secondly, we give out the lower estimation of unknown function of another nonlinear integral inequality. Finally, we discuss the upper and lower bounds of a linear integral inequality by adopting novel analysis techniques, such as change of variable, amplification method, differential and integration.

scholarly journals Nonlinear Inequalities with Double Riesz Potentials

2021 ◽  
Author(s):  
Marius Ghergu ◽  
Zeng Liu ◽  
Yasuhito Miyamoto ◽  
Vitaly Moroz
Keyword(s):  
Integral Inequality ◽  
Riesz Potentials ◽  
Nonlinear Integral Inequality ◽  
Optimal Decay ◽  
Nonnegative Solutions

AbstractWe investigate the nonnegative solutions to the nonlinear integral inequality u ≥ Iα ∗((Iβ ∗ up)uq) a.e. in ${\mathbb R}^{N}$ ℝ N , where α, β ∈ (0, N), p, q > 0 and Iα, Iβ denote the Riesz potentials of order α and β respectively. Our approach relies on a nonlocal positivity principle which allows us to derive optimal ranges for the parameters α, β, p and q to describe the existence and the nonexistence of a solution. The optimal decay at infinity for such solutions is also discussed.

Ulam’s-Type Stability of First-Order Impulsive Differential Equations with Variable Delay in Quasi–Banach Spaces

2018 ◽  
Vol 19 (5) ◽  
pp. 553-560 ◽  
Author(s):  
JinRong Wang ◽  
Akbar Zada ◽  
Wajid Ali
Keyword(s):  
Differential Equations ◽  
Finite Number ◽  
Banach Spaces ◽  
Integral Inequality ◽  
Impulsive Differential Equations ◽  
Variable Delay ◽  
First Order ◽  
Variable Delays ◽  
Ulam’S Type Stability ◽  
First Time

AbstractIn this paper, Ulam’s-type stabilities are studied for a class of first-order impulsive differential equations with bounded variable delays on compact interval with finite number of impulses. Results of stability are proved via newly established integral inequality of Bellman–Grönwall–Bihari type with delay for discontinuous functions. Using this inequality for the first time and assumption of $\alpha$-H$\ddot{o}$lder’s condition instead of common Lipschitz condition is novelty of this paper. Moreover, solution is obtained in quasi–Banach spaces which is best suited for obtaining results under the assumptions of $\alpha$-H$\ddot{o}$lder’s condition.

scholarly journals Integral inequalities of Gronwall type for piecewise continuous functions

1997 ◽  
Vol 10 (1) ◽  
pp. 89-94 ◽  
Author(s):  
Drumi D. Bainov ◽  
Snezhana G. Hristova
Keyword(s):  
Differential Equations ◽  
Integral Inequality ◽  
Initial Value Problem ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Continuous Functions ◽  
Integral Inequalities ◽  
Initial Value ◽  
Volterra Type ◽  
Piecewise Continuous

In this paper we generalize the integral inequality of Gronwall and study the continuous dependence of the solution of the initial value problem for nonlinear impulsive integro-differential equations of Volterra type on the initial conditions.

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