Abstract
Abstract In this paper, some new types of nonlinear integral inequalities on time scales with ‘maxima’, which provide explicit bounds on unknown functions, are established. The importance of these integral inequalities is given by their wide applications in qualitative investigations of differential equations with ‘maxima’. An example is also presented to illustrate our results. MSC:34A40, 26D15, 39A13.
Highlights
1 Introduction The theory of time scales was created by Hilger [ ] in order to unify continuous and discrete analysis and in order to extend those theories to other kinds of the so-called dynamic equations
Many authors have expounded on various aspects of the theory of dynamic equations on time scales
Differential equations with ‘maxima’ are a special type of differential equations that contain the maximum of the unknown function over a previous interval
Summary
The theory of time scales (closed subsets of R) was created by Hilger [ ] in order to unify continuous and discrete analysis and in order to extend those theories to other kinds of the so-called dynamic equations. Let the following conditions be satisfied: (i) The function α ∈ Crd(T , R+) is strictly increasing.
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