Abstract
New nonlinear integral inequalities (NII) are presented in this paper. Based on mathematical analysis technique, several estimation results are obtained, which not only complement the aforementioned results, but also generalize the inequalities to the more general nonlinearities. As an application, they can be employed to estimate the bound on the solutions of power integro-differential equations (IDE).
Highlights
As everyone knows, there exists a class of mathematical models described by differential equations, such as Malthus population model
Integral inequalities are significant for investigating the boundedness, stability, asymptotic behavior of solutions to differential equations
Gronwall [1] put forward the well-known Gronwall inequality to estimate the solution of linear differential equation
Summary
There exists a class of mathematical models described by differential equations, such as Malthus population model. Integral inequalities are significant for investigating the boundedness, stability, asymptotic behavior of solutions to differential equations. Gronwall [1] put forward the well-known Gronwall inequality to estimate the solution of linear differential equation.
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