[PDF] Top 20 Nonlinear integral inequalities with delay for discontinuous functions and their applications

... Gronwall-Bellman integral inequalities and their various linear and nonlinear gen- eralizations, involving continuous or discontinuous functions, play very important roles in ... See full document

... In this section, we will present two examples in order to illustrate the validity of the above results. In the first example, we will try to prove the global existence of the solu- tions of a delay differential ... See full document

... and integral equations, one often needs some kinds of inequalities, such as Gronwall- like inequalities; these inequalities and their various linear and nonlinear generalizations are ... See full document

... new nonlinear integral inequalities Bellman-Bihari type with delay for discontin- uous functions integro-sum inequalities; impulse integral ...Some applications of ... See full document

... The integral inequalities which provide explicit bounds on unknown functions play an im- portant role in the development of the theory of differential and integral ...and nonlinear ... See full document

... some delay nonlinear integral inequalities, so, the inequalities proved in [5] are not directly applicable in the study of delay nonlinear dif- ferential ...new ... See full document

... generalized 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 unknown ... See full document

... Various applications of this result to the study of stability of the solution of lin- ear and nonlinear differential equations may be found in Bellman ...Numerous applications to existence and ... 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

... where the functions, a(x, y), h(x, y) p, q and g are as in The- orem 3.1, M is nonnegative continuous function on D and nondecresing. If u(x, y),(x, y) ∈ D , is any solution of (4.1), then by plugging (4.2) in ... See full document

... Consider nonlinear system ...increasing functions with ’ (t) ≤ k, a (t) ≤ t, a (0) = 0, ∀ t Î I, k be positive constants; then all solutions of Equation ... See full document

... Integral inequalities involving functions of one independent variable, which provide explicit bounds on unknown functions play a fundamental role in the development of the theory of ... 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 properties of solutions of ... See full document

... such inequalities are studied by an iteration argument, and the estimation formulas are expressed by a complicated power series which are some- times not very convenient for ...Henry-type inequalities and ... See full document

... solve integral in- equalities of Henry-Gronwall type, then he got the explicit bounds with a quite simple for- mula, similar to the classic Gronwall-Bellman ... See full document

... The integral inequalities play a fundamental role in the study of existence, uniqueness, boundedness, stability, invariant manifolds, and other qualitative properties of solutions of the theory of di ff ... See full document

... constant delay was considered by Bainov and Hristova in ...with nonlinear functions in ...the functions (kernels) involved in the integrals are regular, even in the case of integrals of ... See full document

... type nonlinear delay integral inequalities for discontinuous functions are established, which can be used as a handy tool in the quantitative and qualitative analysis of ... See full document

... This paper investigates integral inequalities for discontinuous functions with two independent variables involving two nonlinear terms. We do not require that ω (u) is in the class ℘ or ... See full document

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