Abstract
Abstract In this paper, some new Gronwall-Bellman type integral inequalities on time scales containing integration on infinite intervals are established. They provide new bounds for unknown functions concerned and can be used as a handy tool in the research of qualitative and quantitative properties of solutions of certain dynamic equations on time scales. MSC:26E70, 26D15, 26D10.
Highlights
1 Introduction The development of the theory of time scales was initiated by Hilger [ ] as a theory capable to contain both difference and differential calculus in a consistent way
Since many authors have expounded on various aspects of the theory of dynamic equations on time scales
Gronwall-Bellman type integral inequalities are of particular importance as such inequalities provide explicit bounds for unknown functions
Summary
The development of the theory of time scales was initiated by Hilger [ ] as a theory capable to contain both difference and differential calculus in a consistent way. Since many authors have expounded on various aspects of the theory of dynamic equations on time scales (for example, see [ – ], and the references therein). We establish some new Gronwall-Bellman type integral inequalities on time scales containing integration on infinite intervals.
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