[PDF] Top 20 Explicit bounds of unknown function of some new weakly singular retarded integral inequalities for discontinuous functions and their applications

... type integral inequalities have regular or continuous integral kernels, but some problems of theory and practicality require us to solve integral inequalities with sin- gular ... See full document

... Retarded Integral inequalities which give us explicit bounds on unknown functions provide a very important device in the study of many qualitative properties of solutions ... See full document

... well-known inequalities, such as the Gronwall type inequality, the Gronwall-Bellman type inequality, the Henry-Gronwall type inequality, the Henry-Bihari type inequality and their variants in retarded form ... See full document

... work, some new generalized retarded nonlinear integral inequalities, which include nonlinear composite functions of unknown functions between iterated integrals, ... See full document

... nonlinear integral inequalities with the unknown function composed with a given function on the left hand side, more than one distinct nonlinear integrals on its right-hand side, and ... See full document

... the bounds given on such inequalities are not directly applicable in the study of some com- plicated retarded inequalities for discontinuous ...establish new ... See full document

... present some new Gronwall-type inequalities. Explicit bounds for the unknown functions concerned are derived based on these inequalities and the properties of the ... See full document

... nonlinear weakly singular retarded Wendroff-type integral inequality with maxima of an unknown function of two ...given functions is used for estimating the boundedness of ... See full document

... Integral inequalities are used as handy tools in the study of the qualitative properties of solutions to differential and integral equations, such as existence, uniqueness, bounded- ness, stability, ... See full document

... linear integral inequality with singular kernel to in- vestigate some qualitative properties for a parabolic differential equation; Sano and Ku- nimatsu [] gave a modified version of the Henry-type ... See full document

... Integral inequalities that give explicit bounds on unknown functions provide a very useful and important device in the study of many qualitative as well as quantitative ... See full document

... In the past few years, many scholars have extended the Gronwall–Bellman inequality and applied it to many aspects. There can be found many generalizations and analogs of it in various cases from literature (see [3–6]). ... See full document

... establish some new nonlinear delay integral inequalities on time scales, which are generalizations of some known continuous inequalities and discrete inequalities in the ... See full document

... broad applications of it in many areas including threshold theory in biology, ecosystems management and orbital transfer of satellite, see ...the integral inequalities for discontinuous ... See full document

... Some new nonlinear integral inequalities of Gronwall type for retarded functions are established, which extend the results Lipovan 2003 and Pachpatte ...These inequalities ... See full document

... type integral inequalities provide a necessary tool for the study of the theory of di ff erential equa- tions, integral equations and inequalities of the various types (please, see Gronwall [1] ... See full document

... discuss some generalized retarded nonlinear integral inequalities, which not only include nonlinear compound function of unknown function but also include retard items, ... See full document

... of integral equations, the fact cannot be denied that Gronwall–Bellman inequality, Bihari inequality, and their various generalizations play a pivotal role in providing precise bounds of dif- ferential, ... See full document

... continuous functions w(u) on [, ∞ ) such that w() =  and w(αu) ≤ w(α)w(u) for all α >  and u ≥ , and the class j consists of all positive, nondecreasing and continuous functions w(u) on (, ∞ ) such ... See full document

... the retarded Volterra-Fredholm type integral equations with maxima in two ...variables. Some results on the boundedness of their solutions are presented, which demonstrate that our results can be ... See full document