[PDF] Top 20 On Nonlinear Integral Inequalities in One variable and Applications

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

... some nonlinear integral inequalities with weakly singular kernel which can be used as tools in deriving boundedness of the solutions of certain fractional differential equations and integral ... See full document

... and integral equations, a lot of integral inequalities, for example [1-12], have been discovered, which play an important role in the research of boundedness, global existence, stability of solutions ... See full document

... retarded nonlinear integral inequalities, where linear case u(t) in integral functions in [4] is changed into the nonlinear case j(u(t)), and the non-retarded case t in [4] is changed ... 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 of nonlinear retarded ... See full document

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

... of nonlinear weakly singular integral inequalities of Wendroff Type which extend some known weakly singular inequalities for functions in two variables and can be used in the analysis of ... 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 ...[15]. ... See full document

... with a general nonlinear term w(u) of u. They assumed that w ∈ ℘ or w ∈ j , where the class ℘ consists of all nonnegative, nondecreasing and continuous functions w(u) on [, ∞ ) such that w() =  and w(αu) ≤ ... 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

... some nonlinear integral inequalities on time scales, which extend some inequalities established by Li and Sheng 8 and Li ...obtained inequalities can be used as important tools in the ... See full document

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

... of nonlinear integral inequalities on time scales with ‘maxima’, which provide explicit bounds on unknown functions, are ...these integral inequalities is given by their wide ... 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 ... 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 basic ... See full document

... As one can see, the established results above mainly deal with Volterra- Fredholm type integral inequalities with maxima in two ...of one variable, if we take k(x, y) = k, a(x, y) = , ... See full document

... Remark 2.11 . If a = 1, we get the Gronwall inequality in two variables (1.2). Theorem 2.12 . Let u, a, and b be nonnegative continuous functions in D and let f be positive and continuous in D. If a/f is nonincreasing ... 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

... 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

... 8 H. Sano and N. Kunimatsu, “Modified Gronwall’s inequality and its application to stabilization problem for semilinear parabolic systems,” Systems & Control Letters, vol. 22, no. 2, pp. 145–156, 1994. 9 H. Ye, J. ... See full document