共查询到20条相似文献,搜索用时 15 毫秒
1.
The purpose of the present note is to establish some new delay integral inequalities, which provide explicit bounds on unknown functions and generalize some results of Li et al. [Some new delay integral inequalities and their applications, J. Comput. Appl. Math. 180 (2005) 191–200]. The inequalities given here can be used to investigate the qualitative properties of certain delay differential equations and delay integral equations. 相似文献
2.
《Mathematical and Computer Modelling》1997,25(1):51-58
In this paper, we consider Gronwall-Bellman type integral inequalities and the corresponding integral equations for scalar functions of several variables involving abstract Lebesque integrals. Some delay and advance effects are also included. Since the inequalities and the equations are in a general form, the results may have different applications. 相似文献
3.
In this paper, we generalize some integral inequalities to more general situations, and the inequalities of Pachpatte type are corollaries of our's. We establish bounds on the solutions, and we show the usefulness of our results in investigating the asymptotic behavior and the stability on the solutions of integral equations, differential equations and integro-differential equations with time delay. 相似文献
4.
YoungHoKIM 《数学学报(英文版)》2005,21(2):423-434
In this paper, we consider a bound on a general version of the integral inequalities for functions and also study the qualitative behavior of the solutions of certain classes of the hyperbolic partial delay differential equations under the integral inequalities. 相似文献
5.
This paper presents retarded integral inequalities of Henry-Gronwall type. Applying these inequalities, we study certain properties of solutions to fractional differential equations with delay. 相似文献
6.
《中国科学 数学(英文版)》2015,(9)
A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications. 相似文献
7.
非线性中立双曲型时滞偏微分方程解的振动性质 总被引:5,自引:0,他引:5
讨论一类多滞量非线性中立双曲型时滞偏微分方程解的振动性质,应用积分不等式和泛函微分方程的某些结果,获得了其一切解振动的一系列充分条件。结论充分表明了时滞量的决定性作用,指出了其与普通双曲型偏微分方程质的差异。 相似文献
8.
A note on certain integral inequalities with delay 总被引:2,自引:0,他引:2
B. G. Pachpatte 《Periodica Mathematica Hungarica》1995,31(3):229-234
In this paper we establish some new integral inequalities with delay, which can be used as tools in the theory of some new classes of differential and integral equations. An application to obtain a bound on the solution of a certain integral equation is also given. 相似文献
9.
10.
非线性中立抛物型偏微分方程系统的振动性定理 总被引:1,自引:0,他引:1
罗李平 《数学的实践与认识》2009,39(6)
研究一类非线性中立抛物型时滞偏微分方程系统解的振动性质,利用积分不等式和泛函微分方程的某些结果,获得了该类系统在第一类边值条件下所有解振动的若干充分条件.结论充分表明振动是由时滞量引起的. 相似文献
11.
Some Generalized Gronwall-like Retarded Inequalities in two independent variables on Time Scales 下载免费PDF全文
In this paper, we establish some new Gronwall-like inequalities in two independent variables which can be used as tools in the theory of integral equations with delay on time scales. 相似文献
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13.
本文考虑形如x(t)=w(t)+∫^t0f(t,s,xs)ds的具无限时滞的Volterra型积分方程。给出了这样一个方程存在唯一整体解的充分条件,并由此导出相应的积分不等式结果。 相似文献
14.
Lászlo Horváth 《Integral Equations and Operator Theory》2003,45(2):155-176
In this paper, we consider a class of integral equations in measure
spaces, and the corresponding integral inequalities. Special cases are Volterra
type integral equations and Gronwall type integral inequalities. We give different
necessary and su.cient, and only su.cient conditions which together
with the Lipschitz condition imply the existence and the uniqueness of solutions
of the considered integral equations. We study the successive approximations
for the considered integral equations. We derive estimates for the
solutions of the studied integral equations and integral inequalities.
Submitted: June 20, 2000?Revised: July 10, 2001 相似文献
15.
In this paper, we prove some sufficient conditions for the local and global existence of fractional nonlinear finite time delay evolution equations whose linear part is the infinitesimal generators of analytic semigroups. The results are obtained by applying the generalized singular versions of integral inequalities under some different conditions on nonlinear term. At last, two examples are given for demonstration. 相似文献
16.
This paper is devoted to the existence of solution for a class of delay fractional differential equations. First we prove some singular integral inequalities. Then using a fixed point theorem of nonlinear alternative Leray–Schauder type, the existence of at least one solution is proved. To illustrate the main result some examples are given. 相似文献
17.
Some new weakly singular integral inequalities of Gronwall-Bellman type are established, which generalized some known weakly singular inequalities and can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. Some applications to fractional differential and integral equations are also indicated. 相似文献
18.
Zareen A. Khan 《Integral Transforms and Special Functions》2020,31(5):412-423
ABSTRACTThis paper investigates some system of integral inequalities of one independent variable on time scales. The conclusion can be obtained by using Hadamard-type fractional differential equations and Greene's method which bring together and expand some integral inequalities on time scales. The established inequalities give explicit bounds on unknown functions which can be utilized as a key in examining the properties of certain classes of partial dynamic equations and difference equations on time scales. As an application, a system of fractional differential equations is considered to explain the value of our results. 相似文献
19.
Some new nonlinear integral inequalities that involve the maximum of the unknown scalar function of one variable are solved. The inequalities considered are generalizations of a classical nonlinear integral inequality of Bihari. The importance of these integral inequalities is defined by their wide applications in qualitative investigations of differential equations with “maxima”, which is illustrated by some direct applications. 相似文献
20.
The present paper obtains two independent variable generalizations of the integral inequalities of Gollwitzer, Langenhop, and Pachpatte. The bounds provided by these inequalities are adequate in many applications in the theory of partial differential and integral equations. 相似文献