Nonlinear Integral Inequalities with Parameter and Applications - Ghrissi, Taoufik; Hammami, M. A. (Journal of Applied Nonlinear Dynamics, 2026)
We discuss the problem of establishing dissipative estimates for certain differential equations for which the usual methods do not work. The aim of this paper are some new nonlinear integral inequalities leading to suitable uniform (with respect to time and the parameter ε ) bounds on the solutions to problems x(t) = f (t,x(t))+gε(t,x(t)), t ≥ 0 where f ,gε : R+ ×Rn →Rn are supposed to be piecewise continuous in time, locally Lipschitz in x, for any fixed ε ≥ 0. These problems are seen as perturbation to x(t) = f (t,x(t)), t ≥ 0. Furthermore, some examples are given to illustrate the applicability of the obtained results. ©2019 L&H Scientific Publishing, LLC. All rights reserved.