[PDF] Top 20 A class of retarded nonlinear integral inequalities and its application in nonlinear differential integral equation

... Gronwall-Bellman inequalities [, ] can be used as important tools in the study of exis- tence, uniqueness, boundedness, stability, and other qualitative properties of solutions of differential equations, ... See full document

... a class of closed-loop control systems, which demonstrates that our results are handy tools to analyze the qualitative properties of solutions of some nonlinear ordinary differential and integral ... See full document

... new retarded nonlinear Volterra-Fredholm type in- tegral inequalities with maxima in two independent variables in Theorem ...of integral equations with ...of retarded nonlinear ... See full document

... generalized retarded nonlinear integral inequalities with iterated integrals are discussed and upper bound estimations of unknown functions are given by analysis ... See full document

... fundamental integral inequalities used in the theory of differential and integral equations on time ...type inequalities by extending some continuous inequalities given in ... 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 lin- ear and ... See full document

... new nonlinear retarded Volterra–Fredholm type integral inequalities on time ...known integral inequalities, but also provide a handy and effective tool for the study of ... See full document

... of differential and integral equations, integral inequalities established by Gronwall [7], Bellman [2] and Pachpatte’s [9, 10] play a fundamental ...these inequalities are further ... See full document

... generalized retarded nonlinear integral inequalities, which not only include nonlinear compound function of unknown function but also include retard items, and give upper bound ... See full document

... Integral inequalities play a dominant role in the study quantitative properties of solutions of differential and inte- gral ...famous inequalities of this type is known as “Gronwall’s ... See full document

... The differential and integral inequalities occupy a very privileged position in the theory of differential and integral ...years nonlinear integral inequalities ... See full document

... of integral equations appear in a wide variety of physical ...the integral equations is one of the oldest problems in the applied mathematics liter- ature and many computational methods are introduced in ... See full document

... new nonlinear integral inequalities are established, which provide a handy tool for analyzing the global existence and boundedness of solutions of differential and integral ... See full document

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

... The purpose of the present paper is to establish some new nonlinear retarded integral inequalities of Gronwall-Bellman type with two variables. We can demonstrate that inequalities 1.4, ... See full document

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

... of integral equations and differential equations. Some linear and nonlinear gen- eralizations ...equations, integral inequalities with weakly singular kernels have attracted more and more ... See full document

... generalized nonlinear Gronwall-Bellman-Type integral inequalities with two variables, which include a non-constant term outside the ...partial differential equations with the initial and ... See full document

... Several integral in- equalities have been established in the case when maxima of the unknown scalar function is involved in the integral; see [–] and the references cited ... See full document

... a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method ...kind integral equation can be reduced to the second kind ... See full document