本文選題：分?jǐn)?shù)微分方程 + 邊值問(wèn)題��； 參考：《湘潭大學(xué)》2017年碩士論文

【摘要】：近些年來(lái),在諸多學(xué)科領(lǐng)域,非線性分?jǐn)?shù)階微分方程有著廣泛的應(yīng)用,而且非線性分?jǐn)?shù)階微分方程邊值問(wèn)題更是微分方程中的一類重要的問(wèn)題.隨著研究?jī)?nèi)容的不斷深化與研究成果不斷呈現(xiàn),非線性分?jǐn)?shù)階微分方程占據(jù)比重越來(lái)越大,其中在微分方程的多個(gè)分支中,邊值問(wèn)題的研究尤其重要,其問(wèn)題的討論依然在這一方面還需進(jìn)一步補(bǔ)充與深入.本文第二章主要探討了如下的具p-Laplacian算子分?jǐn)?shù)階微分方程兩點(diǎn)邊值問(wèn)題正解的存在性與唯一性.其中α ∈ (1,2), β∈(0,1),D0+α是α階Riemman-iouville分?jǐn)?shù)導(dǎo)數(shù),f是連續(xù)函數(shù).Φp是p-Laplacian算子.本文第三章主要探討了如下的具p-Laplacian算子分?jǐn)?shù)階微分方程邊值問(wèn)題正解的存在性與唯一性.其中,3α≤4,0β≤1,0μ1.D0+α是α階Riemman-Liouville分?jǐn)?shù)導(dǎo)數(shù).f是連續(xù)函數(shù),Φp是p-Laplacian算子.在第二章、第三章中,我們首先討論p-Laplacian算子在非負(fù)有界區(qū)間上的一些性質(zhì)與集合與集合的關(guān)系,然后通過(guò)給定非負(fù)函數(shù)a及非線性函數(shù)f的一些適定條件,結(jié)合由微分方程轉(zhuǎn)換為積分方程的格林函數(shù),采用非緊測(cè)度與不動(dòng)點(diǎn)定理給出了上述問(wèn)題的正解存在唯一性準(zhǔn)則。
[Abstract]:In recent years, nonlinear fractional differential equations have been widely used in many disciplines, and the boundary value problems of nonlinear fractional differential equations are one of the most important problems in differential equations. With the deepening of the research contents and the continuous presentation of the research results, the proportion of nonlinear fractional differential equations is increasing, among which the study of boundary value problems is particularly important in many branches of differential equations. The discussion of its problem still needs to be further supplemented and deepened in this respect. In chapter 2, we discuss the existence and uniqueness of positive solutions for two-point boundary value problems of fractional differential equations with p-Laplacian operators. Where 偽 鈭，

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