泛函积分方程的正解与应用

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1、502Vol.50,No.220073ACTAMATHEMATICASINICA,ChineseSeriesMar.,2007:0583-1431(2007)02-0363-10:A  266033E-mail:zhilinyang@qtech.edu.cn
418008E-mail:weigengping@yahoo.com.cn!"#$%&,(*+,-./0123.45678:(;<./0-.

2、=>?@231AB,5678DEFGHIJKLMNOPQRST178.+,-./0;23;-.=>?@MR(2000)V45G10,45M20,34B08,47H07WO715.15PositiveSolutionsofaFunctionalIntegralEquationandApplicationsZhiLinYANGDepartmentofMathematics,QingdaoTechnologicalUniversity,Qingdao266033,P.R.ChinaE-mail:zhilin

3、yang@qtech.edu.cnGengPingWEIDepartmentofMathematics,HuaihuaCollege,Huaihua418008,P.R.ChinaE-mail:weigengping@yahoo.com.cnAbstractWestudytheexistenceofpositivesolutionsforafunctionalintegralequationusingafixedpointtheoremofexpansionandcompressiontypeinacone.Finallyth

4、emainresultsareusedtoestablishsomeexistenceresultsforpositivesolutionsofintegralboundaryvalueproblemsforordinarydifferentialequations.TheresultspresentedsubstantiallygeneralizeandimprovesomerecentonesduetoMaetal.Keywordsfunctionalintegralequation;positivesolution;in

5、tegralboundaryvalueprob-lemMR(2000)SubjectClassification45G10,45M20,34B08,47H07ChineseLibraryClassificationO715.150!n11u(t)=K(t,s)g(s)f(s,u(s))ds+ϕi(t)u(τ)dαi(τ),(1)0i=10:2005-07-08;:2006-03-30 :"#$ (J06P05)364%%XÆY50+++++&K∈C([

6、0,1]×[0,1],R)(R=[0,+∞)),f∈C([0,1]×R,R),g∈C([0,1],R),g(t)≡0;ϕi∈C[0,1]'ϕi(t)>0,∀t∈(0,1)(i=1,2,...,n);αi![0,1],1![0,1)(,!t=1,αi(0)=0(i=1,2,...,n);0u(τ)dαi(τ)Riemann–Stieltjes(i=1,2,...,n).αi≡0(i=1,2,...,n),g(t)≡1,*(1)[0,1]Hammerstein1u(t)

7、=K(t,s)f(s,u(s))ds,(2)0!(1)(2)+"#.,!-.,(2)$/0%&'"Sturm–[1],[2]Liouville#()1$%,2!34*+&
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