某些线性微分方程的解析解和相应非线性方程的正解.pdf

《某些线性微分方程的解析解和相应非线性方程的正解.pdf》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、˖ڍመ੾᝶஠ڙጲhttp://www.paper.edu.cn某些线性微分方程的解析解和相应非线性方程的正解赵增勤曲阜师范大学数学科学学院，曲阜273165摘要：对于某些具有泛函边界条件的线性微分方程，通过格林函数给出了解的解析表达式.利用得到的格林函数，研究了具有可数多个点的非局部边界条件和积分边界条件下的相应超线性方程正解的存在性.关键词：应用数学；解析解；线性泛函边界条件；格林函数；正解中图分类号：O175.14Exactsolutionsofsomelineardierentialequationsa

2、ndpositivesolutionsofthecorrespondingnonlinearequationsZHAOZengqinSchoolofMathematicalSciences,QufuNormalUniversity,Qufu273165Abstract:ExactexpressionsofthesolutionsforsomelineardierentialequationswithfunctionalboundaryconditionsaregivenbytheGreen'sfunction

3、s.UsingGreen'sfunctionsobtainedweinvestigateexistenceofpositivesolutionsforthecorrespondingsuperlinearequationswithcountablymanypointsandintegralboundaryconditions.Keywords:Appliedmathematics;Exactsolution;linearfunctionalboundarycondition;Green'sfunction;po

4、sitivesolution.0IntroductionandthemainresultsThetheoryofnon-localboundaryvalueproblemshasbeenemergingasanimportantareaofinvestigationsinrecentyears.Theinvestigationofequationu00+f(t;u)=0withnon-localboundaryconditions(multi-pointorintegralboundaryconditions)

5、canbeseenin[1,2,3,4,5,6,7,8]anditsreferences.Theinvestigationofone-dimensionalp-Laplaciannon-localboundaryproblemscanbeseenin[9,10,11,12]anditsreferences.Butconclusionsof基金项目：ResearchsupportedbytheNationalNaturalScienceFoundationofChina(11571197)，andtheDocto

6、ralProgramFoundationofEducationMinistryofChina(20133705110003)作者简介：ZhaoZengqin(1955-),male，professor，majorresearchdirection：Nonlinearfunctionalanalysisanditsapplication.-1-˖ڍመ੾᝶஠ڙጲhttp://www.paper.edu.cntheequation002u+ku=f(t;u);atb;(0.1)withnon-localboun

7、daryconditionsareless,seenin[13,14].Thispaperrstinvestigatestheexactsolutionsofthelinearequation002u+ku=h(t);atb;(0.2)withtheboundaryconditions00u(a)u(a)=F1(u)+c1; u(b)+u(b)=F2(u)+c2:(0.3)WedenotetheuniquesolutionbyitsGreen'sfunction.Afterthat,weappl

8、ytheresultsobtainedtostudythenonlinearboundaryvalueproblem(0.1)(0.3).Werelatethefollowingsymbolsandterminologies.xxThehyperbolicsineandthehyperboliccosinearedenotedbysinh(x)=eeand2xxcosh(x)=e