本文選題：脈沖效應(yīng)　切入點(diǎn)：微分耦合系統(tǒng)　出處：《中國礦業(yè)大學(xué)》2017年碩士論文

【摘要】：微分方程邊值問題是數(shù)學(xué)基礎(chǔ)理論和應(yīng)用研究中的一個(gè)重要分支.隨著研究的逐漸深入,脈沖微分方程邊值問題引起了眾多學(xué)者的關(guān)注,該類方程廣泛地應(yīng)用在航天、工程力學(xué)、材料以及控制等眾多學(xué)科領(lǐng)域當(dāng)中.此外,分?jǐn)?shù)階微分方程邊值問題也是目前數(shù)學(xué)工作者關(guān)注的熱點(diǎn)問題之一.本文研究了幾類帶脈沖項(xiàng)的耦合系統(tǒng)邊值問題弱解的存在性,全文一共分為四章,具體內(nèi)容安排如下:在第一章緒論中,介紹了本課題相關(guān)工作的研究背景和研究意義,概括了相關(guān)問題的研究現(xiàn)狀,最后闡述了本文的研究內(nèi)容.在第二章中,介紹了山路引理,并且利用山路引理研究了 一類整數(shù)階帶p-Laplacian算子的脈沖耦合系統(tǒng)的弱解的存在性問題.在第三章中,運(yùn)用山路引理,研究了一類分?jǐn)?shù)階脈沖耦合系統(tǒng)弱解的存在性與多解性問題.在第四章中,對本文工作進(jìn)行了總結(jié),并且對后續(xù)問題進(jìn)行了展望.本文的創(chuàng)新點(diǎn)主要體現(xiàn)在下述兩個(gè)方面:首先,p-Laplacian算子在p = 2時(shí)為二階線性算子,研究的問題退化為二階線性耦合系統(tǒng)的問題,因此本文較前人的工作更具一般性,推廣了一類微分方程系統(tǒng)邊值問題的研究結(jié)果.其次,分?jǐn)?shù)階脈沖微分系統(tǒng)的研究目前相對較少,本文在前人工作基礎(chǔ)上,研究了一類分?jǐn)?shù)階脈沖耦合系統(tǒng)弱解的存在性問題,因此,本文在某種程度上推廣和豐富了分?jǐn)?shù)階微分方程邊值問題研究和脈沖耦合系統(tǒng)的已有研究成果。
[Abstract]:Boundary value problems of differential equations is an important branch of mathematical theory and application research. With the deepening of the investigation, the problem has aroused the concern of many scholars of impulsive differential equation boundary value, the equations are widely used in aerospace, mechanical engineering, material control and many other disciplines. In addition, fractional differential boundary value problem is currently one of the hot issues of mathematics educators pay close attention to. The existence of the weak solutions of coupling system is studied in this paper several kinds of impulses of the boundary value, this paper is divided into four chapters, the main contents are as follows: in the first chapter, introduces the related work of the research background and research significance and summarizes the current research status of related problems, finally elaborated the research content of this paper. In the second chapter, introduces the mountain pass lemma, and the mountain pass lemma is studied for a class of integer order with p-Laplac The existence of weak solutions of pulse coupling system of the Ian operator. In the third chapter, using the mountain pass lemma is studied for a class of fractional impulsive coupling system of the existence of weak solutions and multiple solutions. In the fourth chapter, the work of this thesis is summarized and the follow-up issues are discussed in this paper. The innovation is mainly reflected in the following two aspects: first, p-Laplacian operator at P = 2 for two order linear operator, the research problem is reduced to two order linear coupling system, this paper compared with the previous work is more general, the promotion of a system of differential equations with boundary value problems of the research results. Secondly, study the fractional order impulsive differential system is relatively small, on the basis of previous work, study a class of fractional impulsive coupling system existence problem, weak solution so this to some extent promote and enrich the fractional order The research on boundary value problems of differential equations and the existing research results of the pulse coupling system.

【學(xué)位授予單位】：中國礦業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.8

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本文編號：1676383