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Gronwall-Bellman-type integral inequalities and applications to BVPs. (English) Zbl 1176.35007

Summary: We establish some new nonlinear Gronwall-Bellman-Ou-Iang type integral inequalities with two variables. These inequalities generalize former results and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of differential equations. Example of applying these inequalities to derive the properties of BVPs is also given.

MSC:

35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
26D15 Inequalities for sums, series and integrals
34B15 Nonlinear boundary value problems for ordinary differential equations
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