On Some New Nonlinear Integral Inequalities of Gronwall- Bellman Type
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In this paper, we establish some new nonlinear integral inequalities ofGronwall-Bellman type. These inequalities generalize some famous inequalities which canbe used in applications as handy tools to study the qualitative as well as quantitativeproperties of solutions of some nonlinear ordinary di erential and integral equations. Moreaccurately we extend certain results which have been proved in A. Abdeldaim and M. Yak-out [1] and H. El-Owaidy, A. A. Ragab, A. Abdeldaim [7] too.
Abstract
In this paper, we establish some new nonlinear integral inequalities ofGronwall-Bellman type. These inequalities generalize some famous inequalities which canbe used in applications as handy tools to study the qualitative as well as quantitativeproperties of solutions of some nonlinear ordinary di erential and integral equations. Moreaccurately we extend certain results which have been proved in A. Abdeldaim and M. Yak-out [1] and H. El-Owaidy, A. A. Ragab, A. Abdeldaim [7] too.
참고문헌 (12)
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- V. Barbu, "Differential Equations" (1985), Ed. Junimca
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- H. T. Gronwall, "Note on the derivatives with respect to a parameter of the solutions of differential equations", Ann. of Math., 20(2), pp.292~296 (1919)
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- B. G. Pachpatte, "Inqualities for Differntial and Integral Equations" (1998), Academic Press
- D. Willett, "On the discrete analogues of some generalization of Gron-wall's inequality", Monatsh, 69, pp.362~367 (1965)