本文選題：三階邊值問(wèn)題　切入點(diǎn)：格林函數(shù)　出處：《山東師范大學(xué)》2017年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：常微分方程邊值問(wèn)題是常微分方程理論研究中最為重要的課題之一.隨著科學(xué)技術(shù)的進(jìn)步與發(fā)展,工程、力學(xué)、天文學(xué)、經(jīng)濟(jì)學(xué)、控制論及生物學(xué)等自然學(xué)科和邊緣學(xué)科領(lǐng)域中的許多實(shí)際問(wèn)題都可歸結(jié)為常微分方程的邊值問(wèn)題.我們知道,尋求微分方程的通解十分困難,故從理論上探討解的存在性及其性態(tài),一直是近年來(lái)研究的熱點(diǎn)問(wèn)題.本文主要研究非線性三階邊值問(wèn)題的存在性.全文共分三章.第一章介紹了研究背景和預(yù)備知識(shí)及重要定理。第二章研究三階兩點(diǎn)邊值問(wèn)題一個(gè)正解、兩個(gè)正解、三個(gè)正解的存在性.令(?),(?),若f_0=0,f_∞=∞(超線性),或者f_0=∞且f_∞=0(次線性),則邊值問(wèn)題(Ⅰ)至少存在一個(gè)正解.若f_0=f_∞=0,則邊值問(wèn)題(Ⅰ)至少有兩個(gè)正解.令(?),(?).假設(shè)存在實(shí)數(shù)d_0,d_1和c且0d_0d_1d_1/γc 使得下列式子滿足 f(x)d_0/D,x∈[0,d_0]f(x)d_1/C,x∈[d_1,d_1/γ],f(x)c/D,x∈[0,c],則邊值問(wèn)題(Ⅰ)至少有三個(gè)正解.第三章研究三階三點(diǎn)邊值問(wèn)題一個(gè)正解、兩個(gè)正解、三個(gè)正解的存在性.令(?),(?),若f_0=0,f_∞=∞(超線性),或者f_0=∞且f_∞=0(次線性),則邊值問(wèn)題(Ⅱ)至少存在一個(gè)正解.若f_0=f_∞=0,則邊值問(wèn)題(Ⅱ)至少有兩個(gè)正解.令(?),(?).假設(shè)存在實(shí)數(shù)d_0,d_1和c且0d_0d_1d_1d_1/γc使得下列式子滿足f(t,u)d_0/D,u∈[0,d_0],f(t,u)d_1/C,u∈[d_1,d_1/γ],f(t,u)c/D,u∈[0,c]邊值問(wèn)題(Ⅱ)至少有三個(gè)正解.
[Abstract]:The boundary value problem of ordinary differential equation is one of the most important subjects in the research of ordinary differential equation theory. With the progress and development of science and technology, engineering, mechanics, astronomy, economics, Many practical problems in natural and marginal disciplines such as cybernetics and biology can be reduced to boundary value problems of ordinary differential equations. Therefore, the existence and behavior of the solution are discussed theoretically. This paper mainly studies the existence of nonlinear third-order boundary value problems. The thesis is divided into three chapters. The first chapter introduces the research background, preparatory knowledge and important theorems. In Chapter 2, we study the third-order second-order problems. A positive solution to the point boundary value problem, Existence of two positive solutions, three positive solutions. What? If f0 _ 鈭，

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