scholarly journals Estimation of Unknown Function of a Class of Nonlinear Integral Inequality

2015 ◽  
Author(s):  
Ouyang Yun ◽  
Wusheng Wang
Keyword(s):  
Integral Inequality ◽  
Unknown Function ◽  
Nonlinear Integral Inequality

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.

A Class of Integral Inequality and Application

2013 ◽  
Vol 785-786 ◽  
pp. 1395-1398 ◽  
Author(s):  
Wu Sheng Wang
Keyword(s):  
Differential Equations ◽  
Upper Bound ◽  
Integral Inequality ◽  
Unknown Function ◽  
Initial Conditions ◽  
Integral Inequalities ◽  
Inequality Technique ◽  
Bound Estimation

We discuss a class of generalized retarded nonlinear integral inequalities, which not only include nonlinear compound function of unknown function but also include retarded items, and give upper bound estimation of the unknown function by integral inequality technique. This estimation can be used as tool in the study of differential equations with the initial conditions.

A Class of Nonlinear Weakly Singularity Wendroff Type Integral Inequality with Two Variables and Application

2014 ◽  
Vol 1008-1009 ◽  
pp. 1493-1496
Author(s):  
Wu Sheng Wang ◽  
Yi Bing Lai
Keyword(s):  
Integral Inequality ◽  
Unknown Function ◽  
Nonlinear Function ◽  
Jensen Inequality ◽  
Composite Function ◽  
Type Integral

In this paper, we establish a nonlinear weakly singularity Wendroff type integral inequality with two variables, which generalizes the unknown function with a variable to composite function of nonlinear function with unknown function with two variables. Under certain conditions, the estimation of unknown function is given by the technique of amplification, variable substitutions, integration and differentiation, discrete Jensen inequality.

scholarly journals A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Jun Zhou
Keyword(s):  
Differential Equation ◽  
Initial Data ◽  
Fractional Differential Equation ◽  
Integral Inequality ◽  
Unknown Function ◽  
Continuous Dependence ◽  
Weak Singularity ◽  
Type Integral ◽  
Fractional Differential ◽  
Continuous Dependence Of Solutions

We discuss on integrable solutions for a generalized Henry-type integral inequality in which weak singularity and delays are involved. Not requiring continuity or differentiability for some given functions, we use a modified iteration argument to give an estimate of the unknown function in terms of the multiple Mittag-Leffler function. We apply the result to give continuous dependence of solutions on initial data, derivative orders, and known functions for a fractional differential equation.

scholarly journals Nonlinear integral inequality in two independent variables

1988 ◽  
Vol 11 (1) ◽  
pp. 115-119
Author(s):  
P. T. Vaz ◽  
S. G. Deo
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Integral Inequality ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential ◽  
Independent Variables ◽  
Nonlinear Integral Inequality ◽  
Nonlinear Inequality ◽  
Two Independent Variables

In this note, the authors obtain a generalization of the integral inequality of Bihari [1] to a nonlinear inequality in two independent variables. With the aid of this inequality a bound for the solution of a nonlinear partial differential equation is established.

Sign in / Sign up

Export Citation Format

Share Document