資源描述：
《分?jǐn)?shù)階微分方程的非局部問(wèn)題》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫(kù)。
1、學(xué)校代碼10530學(xué)號(hào)201510111119分類號(hào)O175密級(jí)公開(kāi)碩士學(xué)位論文分?jǐn)?shù)階微分方程的非局部問(wèn)題學(xué)位申請(qǐng)人賈蘭蘭指導(dǎo)老師周勇教授學(xué)院名稱數(shù)學(xué)與計(jì)算科學(xué)學(xué)院學(xué)科專業(yè)數(shù)學(xué)研究方向微分方程與動(dòng)力系統(tǒng)二〇一八年四月十日分?jǐn)?shù)階微分方程的非局部問(wèn)題學(xué)位申請(qǐng)人賈蘭蘭導(dǎo)師姓名及職稱周勇教授學(xué)院名稱數(shù)學(xué)與計(jì)算科學(xué)學(xué)院學(xué)科專業(yè)數(shù)學(xué)研究方向微分方程與動(dòng)力系統(tǒng)學(xué)位申請(qǐng)級(jí)別理學(xué)碩士學(xué)位授予單位湘潭大學(xué)論文提交日期2018{04{10NonlocalProblemsofFractionaldifferentialEquationsCandidateLanlanJiaSupervisorProf.
2、YongZhouCollegeSchoolofMathematicsandComputationalScienceProgramMathematicsSpecialityDi erentialEquationsandDynamicalSystemsDegreeMasterofScienceUniversityXiangtanUniversityDateApril10th,2018摘要對(duì)于分?jǐn)?shù)階發(fā)展方程的非局部邊值問(wèn)題,我們得到了在半群是緊和非緊的情形下其適度解的存在性.本文主要討論了一類具有Caputo導(dǎo)數(shù)的分?jǐn)?shù)微分方程的非線性非局部邊值問(wèn)題.第二章中,我們先討論分?jǐn)?shù)階發(fā)展方程
3、的初邊值問(wèn)題,并得到其適度解形式,然后定義一個(gè)解算子:(?,將初值?0∈映成初邊值問(wèn)題的適度解集,從而非線性非局部問(wèn)題等價(jià)為一種抽象包含?(?0)∈?((?0)),然后利用Benevieri-Furi度理論的同倫不變性給出了半群是緊的情形下適度解的存在性.第三章中,當(dāng)半群非緊時(shí),我們利用非緊測(cè)度的方法,當(dāng)非線性項(xiàng)?滿足Lipschitz連續(xù)條件時(shí),得到了非局部問(wèn)題適度解的存在性.關(guān)鍵詞:分?jǐn)?shù)階發(fā)展方程;Caputo導(dǎo)數(shù);Cauchy問(wèn)題;多值映射;適度解.IAbstractForthenonlocalboundaryvalueproblemsoffractionalevol
4、utionequations,weobtaintheexistenceofmildsolutionsinthecasesthatthesemigroupiscompactandnoncompact,respectively.Thispaperisconcernedwiththenonlinearandnonlocalboundaryproblemsofaclassoffractionaldi erentialequationswithCaputoderivatives.Inchapter2,we rstlystudytheformofmildsolutionsforinitia
5、lboundaryvalueproblemofthefractionalevolutionequation,toobtainthede nitionofmildsolutions,andde neasolutionoperator:(?,whichmapstheinitialvalue?0∈tothesetofthemildsolutionsforinitialboundaryvalueproblem.Thenthenonlinearnonlocalproblemisequivalenttoanabstractinclusionof?(?0)∈?((?0)).Thenweo
6、btaintheexistenceofmildsolutionsinthecasethatthesemigroupiscompact,byusingthehomotopyinvarianceofBenevieri-Furidegreetheory.Inchapter3,weusethemethodofnoncompactmeasurestoacquiretheexistenceofmildsolutionsfornonlinearandnonlocalproblemwhenthenonlinearityfsatis estheLipschitzcontinuousconditi
7、on.Inthecasethatthesemigroupisnoncompact.Keywords:Fractionalevolutionequations;Caputoderivative;Cauchyprob-lem;Multi-valuedmapping;Mildsolution.II目錄第一章緒論...................................11.1研究背景及現(xiàn)狀..............................11.2本文的主要工作........
