几类具有偏差变元的高阶积分—微分方程解的渐近性
发布时间：2018-10-09 21:48
【摘要】：对于积分一微分方程解的渐近性的研究是方程领域的重要研究问题,由于在某些特定的条件下,利用积分不等式,可以得到非线性积分一微分方程解的渐近状态与某个齐次方程解的渐近状态一致.因此在推广的过程中也产生了系统的研究类似问题的统一方法.Gronwall-Bellman和Bihari积分不等式及其推广在积分一微分方程解的渐近性方面起着重要的作用.许多学者和研究者为了达到不同的目标,己经在过去几年内建立了一些重要的Gronwall-Bellman和Bihari积分不等式,并用此研究了几类积分-微分方程解的渐近性.在2004年,孟凡伟[6]研究了下列的具有偏差变元的二阶积分一微分方程解的渐近性:在2013年,孟凡伟和姚建丽[7]研究了下列形式的具有偏差变元的高阶非线性积分-微分方程解的渐近性:本文在此基础上,利用推广的Gronwall-Bellman和Bihari积分不等式,对上述积分一微分方程进行推广,并研究了其解的渐近状态,得到一些新的结果.最后,通过一种推广的离散Bihari型不等式,我们可以得到一类三阶非线性差分方程的解的有界性与渐近性.根据内容本论文由以下五章构成:第一章 绪论,介绍本论文研究的主要问题和背景.第二章 利用新的Gronwall-Bellman和Bihari积分不等式,对积分-微分方程进行推广,得到具有偏差变元的三阶积分-微分方程,并研究其解的渐近性:其中a=a(t)是在R+=[0, ∞)上的正的连续可微函数,使得a(0) = 1;b (t),c(t),d(t)是在R+上的连续函数;f∈C[R+×R7,R]和g∈C[R+2×R6,R];α(t),β(t)是连续可微的并且满足α(t)≤t,β(t)≤t;α'(t)0,β'(t)0并且α(t),β(t)最终是正的.第三章利用新的Gronwall-Bellman和Bihari积分不等式,对积分-微分方程进行推广,得到具有偏差变元的高阶积分-微分方程,并研究其解的渐近性:其中p(t)是定义在R+=[0,∞)上的一个可微函数,并且p(t)0,p(0)=1;ci=ci(t)(i=1,2,...,n)是R+上的连续函数;φ∈C[R+,R],α(t)≤t,α'(t0,β(t)≤t,β'(t) 0,并且α(t),β(t)最终是正的,f∈C[R+×R2n+1, R],g∈C[R+2×Rn,R].第四章 利用新的Gronwall-Bellman和Bihari积分不等式,对积分-微分方程进行推广,得到具有偏差变元的高阶非线性积分-微分方程,并研究其解的渐近性:其中p=p(t)是一个定义在R+=[0,∞)上的正的连续可微函数,使得p(0) = 1;ci(t)(i=1,2,…,n)是R+上的连续函数;f∈C[R+×R2n+1,R]并且g∈C[R+2×R2n,R];α(t),β(t)是连续可微的,并且满足α(t)≤t,β(t)≤t;α'(t)0, β'(t)0同时α(t),β(t)最终是正的.第五章通过一种推广的离散Bihari型不等式,研究一类三阶非线性差分方程解的有界性和渐近性:△(r2(n)△(r1(n)△(xp(n))))+f(n,x(n))=0其中n ∈N+(n0) = {n0,n0 + 1,...},n0∈N+, △为向目前差分算子,r(n)是实序列,f是定义在N(n0) × R × R上的实值函数.
[Abstract]:The study of asymptotic behavior of solutions of integro-differential equations is an important problem in the field of equations. The asymptotic state of the solution of the nonlinear integro-differential equation is consistent with that of the solution of a homogeneous equation. Therefore, in the process of generalization, the unified method of studying similar problems. Gronwall-Bellman and Bihari integral inequalities and their generalization also play an important role in the asymptotic behavior of the solutions of integro-differential equations. In order to achieve different goals, many scholars and researchers have established some important Gronwall-Bellman and Bihari integral inequalities in the past few years, and used this to study the asymptotic behavior of solutions of several kinds of integro-differential equations. In 2004, Meng Fanwei [6] studied the asymptotic behavior of solutions to second order integro-differential equations with deviating arguments: in 2013, Meng Fanwei and Yao Jianli [7] have studied the asymptotic behavior of solutions of higher order nonlinear integro-differential equations with deviating arguments: in this paper, we use generalized Gronwall-Bellman and Bihari integral inequalities. In this paper, we generalize the above integro-differential equation and study the asymptotic state of its solution, and obtain some new results. Finally, by means of a generalized discrete Bihari type inequality, we can obtain the boundedness and asymptotic behavior of solutions for a class of third-order nonlinear difference equations. According to the content, this paper is composed of the following five chapters: the first chapter introduces the main problems and background of this paper. In chapter 2, by using the new Gronwall-Bellman and Bihari integral inequalities, we generalize the integro-differential equations and obtain the third-order integro-differential equations with deviating arguments. The asymptotic behavior of the solution is studied: where a (t) is a positive continuous differentiable function on R = [0, 鈭瀅. Such that a (0) = 1b (t) c (t) d (t) is a continuous function on R f 鈭，
本文编号：2260904
[Abstract]:The study of asymptotic behavior of solutions of integro-differential equations is an important problem in the field of equations. The asymptotic state of the solution of the nonlinear integro-differential equation is consistent with that of the solution of a homogeneous equation. Therefore, in the process of generalization, the unified method of studying similar problems. Gronwall-Bellman and Bihari integral inequalities and their generalization also play an important role in the asymptotic behavior of the solutions of integro-differential equations. In order to achieve different goals, many scholars and researchers have established some important Gronwall-Bellman and Bihari integral inequalities in the past few years, and used this to study the asymptotic behavior of solutions of several kinds of integro-differential equations. In 2004, Meng Fanwei [6] studied the asymptotic behavior of solutions to second order integro-differential equations with deviating arguments: in 2013, Meng Fanwei and Yao Jianli [7] have studied the asymptotic behavior of solutions of higher order nonlinear integro-differential equations with deviating arguments: in this paper, we use generalized Gronwall-Bellman and Bihari integral inequalities. In this paper, we generalize the above integro-differential equation and study the asymptotic state of its solution, and obtain some new results. Finally, by means of a generalized discrete Bihari type inequality, we can obtain the boundedness and asymptotic behavior of solutions for a class of third-order nonlinear difference equations. According to the content, this paper is composed of the following five chapters: the first chapter introduces the main problems and background of this paper. In chapter 2, by using the new Gronwall-Bellman and Bihari integral inequalities, we generalize the integro-differential equations and obtain the third-order integro-differential equations with deviating arguments. The asymptotic behavior of the solution is studied: where a (t) is a positive continuous differentiable function on R = [0, 鈭瀅. Such that a (0) = 1b (t) c (t) d (t) is a continuous function on R f 鈭，
本文编号：2260904
本文链接：https://www.wllwen.com/kejilunwen/yysx/2260904.html
