Gronwall-like Inequalities on Time Scales with Applications
نویسنده
چکیده
Some new nonlinear dynamic integral inequalities of Gronwall type for retarded functions are established. These inequalities can be used as basic tools in the study of certain classes of functional dynamic equations as well as dynamic delay equations. AMS Subject Classification: 39A10.
منابع مشابه
Some new variants of interval-valued Gronwall type inequalities on time scales
By using an efficient partial order and concept of gH-differentiability oninterval-valued functions, we investigate some new variants of Gronwall typeinequalities on time scales, which provide explicit bounds on unknownfunctions. Our results not only unify and extend some continuousinequalities, but also in discrete case, all are new.
متن کاملGronwall-OuIang-Type Integral Inequalities on Time Scales
OuIang inequalities and their generalizations have proved to be useful tools in oscillation theory, boundedness theory, stability theory, and other applications of differential and difference equations. A nice introduction to continuous and discrete OuIang inequalities can be found in 1, 2 , and studies in 3–5 give some of their generalizations to multiple integrals and higher-dimensional space...
متن کاملSome New Gronwall-Bellman-Type Inequalities on Time Scales and Their Applications
In this work, we investigate some new Gronwall-Bellman type dynamic inequalities on time scales in two independent variables, which provide a handy tool in deriving explicit bounds on unknown functions in certain dynamic equations on time scales. The established results generalize the main results on integral inequalities for continuous functions in [1] and their corresponding discrete analysis...
متن کاملNonlinear Dynamic Inequalities of Gronwall-Bellman Type on Time Scales
The main aim of this paper is to establish some new explicit bounds of solutions of a certain class of nonlinear dynamic inequalities (with and without delays) of Gronwall-Bellman type on a time scale T which is unbounded above. These on the one hand generalize and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of delay dynami...
متن کاملGeneralized Delay Integral Inequalities In Two Independent Variables On Time Scales
Abstract: In this paper, we discuss some new Gronwall-Bellman type delay integral inequalities in two independent variables on time scales, which contain arbitrary nonlinear items on unknown functions outside the integrals as well as inside the integrals. The inequalities established have different forms compared with the existing GronwallBellman type inequalities so far in the literature. As a...
متن کامل