發(fā)布時間：2018-06-22 00:15

  本文選題：非線性分數(shù)階微分方程 + m點邊值問題　； 參考：《曲阜師范大學》2017年碩士論文

【摘要】：本文研究的是帶有擾動項的非線性微分方程的解.通過專家學者對非線性整數(shù)階常微分方程的不斷研究,我們對其已經(jīng)非常了解,并且在物理學,生物學,經(jīng)濟學等許多領域得到了廣泛的應用.隨著科學的發(fā)展和不斷地深入研究,我們通過對非線性常微分方程加以推廣與改造,在帶有擾動項的非線性微分方程方面進行了深入的研究,并且也取得了突破性的研究成果,如文獻[1]運用Schauder不動點定理證明了帶有擾動項的非線性微分方程解的存在性.文獻[2],[3]都是運用錐拉伸與壓縮不動點定理得到了所研究方程解的存在性.本文受文獻[1]-[5]的啟發(fā),對帶有擾動項的非線性微分方程進行了研究.根據(jù)內容,本文分為以下三章:第一章:主要是介紹本文將要用到的一些基本定義和一些與本文證明有關的引理.第二章:考慮帶有擾動項的非線性分數(shù)階微分方程邊值問題解的存在性,其中D0α+u(t)是Riemann-Liouville分數(shù)階導數(shù),α≥ 2,1 ≤α-β ≤n - 1,n - 1 ≤ α ≤ n,ηi ≥ 0(i = 1,2,...,m - 2),0 ξ_1 ξ_2 … ξ_(m-2) 1,f :(0,1) × (0,∞) × (0,∞)→(0,∞)連續(xù),e(t)∈L1([0,1],R)可能變號.運用Schauder不動點定理,得到解的存在性,最后給出應用.第三章:考慮帶有擾動項的非線性分數(shù)階微分方程的特征值問題其中λ是正實參數(shù),D1qx(t)是Riemann-Liouville分數(shù)階導數(shù),q ≥ 2,n-1 ≤q ≤n,i ∈ N, 0 ≤ i ≤ n - 2, a_j ≥ 0(j = 1, 2,..., m - 2), 0 b_1 b_2 … b_(m-2) 1, (?),f ∈ C(0,1) × (0,∞) → [0,∞)并且在t = 0,1處奇異,e(t) ∈ L~1([0,1],R)可能變號.運用錐拉伸與壓縮不動點定理,得到解的存在性,作為應用給出相應的例子.
[Abstract]:In this paper, we study the solutions of nonlinear differential equations with perturbed terms. Through the continuous study of nonlinear integer order ordinary differential equations by experts and scholars, we have been very familiar with them, and have been widely used in many fields such as physics, biology, economics and so on. With the development of science and the research of the nonlinear ordinary differential equation, we have made a thorough research on the nonlinear differential equation with perturbation term, and have also made a breakthrough research result. For example, in reference [1], the existence of solutions for nonlinear differential equations with perturbed terms is proved by using Schauder fixed point theorem. In references [2] and [3], the existence of solutions to the equations studied is obtained by using the fixed point theorems of cone stretching and compression. In this paper, the nonlinear differential equations with perturbed terms are studied, inspired by references [1]-[5]. According to the content, this paper is divided into the following three chapters: the first chapter: mainly introduces some basic definitions and some Lemma related to the proof of this paper. Chapter 2: consider the existence of solutions for the boundary value problems of nonlinear fractional differential equations with perturbed terms, where D 0 偽 u (t) is the fractional derivative of Riemann-Liouville, 偽 鈮，

本文編號：2050668