【摘要】：在對分數(shù)階單個系統(tǒng)解的情況的研究基礎(chǔ)上,相應(yīng)的分數(shù)階耦合系統(tǒng)解的存在情況也得到越來越多的關(guān)注.本文受此啟發(fā),在一類非線性分數(shù)階系統(tǒng)邊值問題正解的存在性研究的基礎(chǔ)上,進而研究了該邊值條件下耦合系統(tǒng)正解的存在情況.所用的主要方法是壓縮映射定理,錐上的不動點定理和Schauder不動點定理等定理以及格林函數(shù)的相關(guān)性質(zhì),探討了分數(shù)階耦合系統(tǒng)在不同條件限制下的正解的存在情況。
[Abstract]:Based on the study of the solution of fractional order single system, more and more attention has been paid to the existence of the corresponding solution of fractional order coupled system. In this paper, based on the study of the existence of positive solutions for a class of nonlinear fractional order boundary value problems, the existence of positive solutions for coupled systems under the boundary value condition is studied. The main methods used are contractive mapping theorem, fixed point theorem and Schauder fixed point theorem on cone, and the related properties of Green's function. The existence of positive solutions of fractional coupled system under different conditions is discussed.
【學位授予單位】：東北師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175.8

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相關(guān)期刊論文 前1條

1 張萌;孫書榮;趙以閣;楊殿武;;一類分數(shù)階微分方程邊值問題正解的存在性[J];濟南大學學報(自然科學版);2010年02期

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本文編號：2204479