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时间:2019-05-11
《具有非分离边界条件的非线性分数阶微分包含弱解的存在性》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
1、CHINESEJoURNALOct.2014Vo1.31N0.5oFENGINEERINGMA,I’HEMATICSdof10.3969/j.issn.1005—3085.2014.05.015ArticleID:1005·-3085(2014)05-0779--12FractionalDirentialInclusionwithNon-separatedBoundaryConditions术ZHOUWen-xue1,2.LIUHai—zhong(1一CollegeofMathematicsandPhysics,LanzhouJia
2、otongUniversity,Lanzhou730070;2-SchoolofMathematicalSciences,Fuda_nUniversity,Shanghai200433)Abstract:Manypracticalproblems,suchaSthosefromphysics,aerospacescience,ecologicalscienceandengineering,needtobedescribedbyfractionaldiferentialequations,SOitisimportanttostudyt
3、heseequationsintheoryandimplement.Inthispaper,underthePettisintegrabilityaSsumption,wediscusstheexistenceofweaksolutiontotheboundaryvalueproblemforaclassofnonlinearfractionaldiferentialinclu—sioninvolvingnon—separatedboundaryconditions.ThediferentialoperatoristheCaputo
4、derivative,andthenonlineartermhaSweaklysequentiallyclosedgraph.TheanalysisreliesonMonch’Sfixedpointtheoremcombinedwiththetechniqueofmeasuresofweaknoncompactness.Finally,anexampleisgiventoillustratetheefectivenessoftheproposedmethod.Keywords:boundaryvalueproblem;fractio
5、naldiferentialinclusion;Caputofractionalderiva-tive;weaksolutionsClassification:AMS(2000)26A33;34B15CLCnumber:O175.8DOCl1InentCOde:A1IntroductionThispaperismainlyconcernedwiththeexistenceresultsforthe%llowingfractionaldiferentialinclusionwithnon—separatedboundarycondit
6、ions{CD。"u:(t)eF(t’:’二三+。≠,入。≠,(1)where17、archfield:theoryandapplicationofnonlinearfunctionalanalysis.F0andationitem:TheNationalNaturalScienceFoundationofChina(11161027;11262009;112261321:theNaturalScienceFoundationofGansuProvince(1308RJZA113):theScientificResearchProjectsinCO-liegesandUniversitiesofGansuProvi8、nce(2013A一043);theFundamentalResearchFundsfortheCansuUniversities(212084;213061);theYouthScienceFoundationofLanzhouJi
7、archfield:theoryandapplicationofnonlinearfunctionalanalysis.F0andationitem:TheNationalNaturalScienceFoundationofChina(11161027;11262009;112261321:theNaturalScienceFoundationofGansuProvince(1308RJZA113):theScientificResearchProjectsinCO-liegesandUniversitiesofGansuProvi
8、nce(2013A一043);theFundamentalResearchFundsfortheCansuUniversities(212084;213061);theYouthScienceFoundationofLanzhouJi
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