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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Nonlinear Integral Inequalities WITH Parameter and Applications

Journal of Environmental Accounting and Management 7(4) (2018) 425--436 | DOI:10.5890/JAND.2018.12.009

Taoufik Ghrissi, M. A. Hammami

Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax Route Soukra, BP 1171, 3000 Sfax, Tunisia

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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 arameter 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.


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