几类新的具有积分跳跃条件的Wendroff型积分不等式

发布时间：2019-05-10 14:00

【摘要】：随着微分方程理论的发展,微分方程在社会科学和自然科学中有着广泛的应用.Gronwall不等式,Gronwall-Bellman不等式及其推广形式是研究微分方程与积分方程解的存在性、稳定性、唯一性、有界性、渐近性和振动性等定性性质的一种重要工具,众多学者对其进行了一系列的推广.众所周知,脉冲微分方程在微分方程理论中占有重要地位,许多作者致力于利用脉冲微分不等式和脉冲积分不等式来考察具有脉冲扰动问题的解的定性性质.Borysenko在[1]中研究了具有两个独立变量的函数的脉冲积分不等式:其中φ(t,x)除了点(ti,xi)外是非负连续的,u(t_i+ 0,x_i + 0)≠u(t_i -0,x_i-0),i = 1,2, ….本文在参考文献[1,3,5,9,15,19,20,21]的基础上,对具有两个独立变量的不连续函数的Wendroff型脉冲积分不等式进行了推广.根据内容本文分为以下三章:第一章 绪论,介绍本文研究的主要问题及其背景.第二章 本章推广出如下的Wendroff型积分不等式:这里m 0, t_0 ≥ 0, x_0 ≥ 0;γ_i= const ≥0,β_i = const ≥ 0, 0≤τ_k≤σ_k≤t_k-t_(k-1),0≤δ_k≤λ_k≤x_k-x_(k-1),对任意的(t,x) ∈Ω,a(t,x)0.且关于(t,x)是非减函数,即(?)(p,g)∈ Ω, (P,Q)∈Ω,当(?)p ≤ P,(?)q ≤ Q时,有a(p,q)≤a(P,Q),并且满足条件:b(t,x)≥0并且b(ζ,η) = 0,若(ζ,η)∈Ωij,i≠j,(?)i,j=1,2,….当t_kt_(k+1),x_kx_(k+1),(?)k=0,1,2,…时,有(t_k,x_k)(t_(k+1),x_(k+1)),且本章得到了更为广泛的结论,为研究偏微分方程解的有界性提供了有力的工具.第三章将第二章中具有积分跳跃条件的Wemdroff型积分不等式推广至带有时滞的且具有积分跳跃条件的二元积分不等式:推广了已有的研究结果,并用这些不等式研究方程解的性质.
[Abstract]:With the development of differential equation theory, differential equation has been widely used in social science and natural science. Gronwall inequality, Gronwall-Bellman inequality and its extended form are to study the existence and stability of solutions for differential equations and integral equations. Uniqueness, bounded, asymptotic and oscillatory are an important tool for qualitative properties, which have been extended by many scholars. As we all know, impulsive differential equations play an important role in differential equation theory. Many authors devote themselves to studying the qualitative properties of solutions with impulsive perturbation problems by using impulsive differential inequalities and impulsive integral inequalities. Borysenko studied the impulsive integral inequality of functions with two independent variables in [1]. Formula: where 蠁 (t, X) in addition to the point (ti,xi), there is a nonnegative continuous, u (t 鈮，

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