含有广义p—Laplace算子具混合边值条件的积分微分方程解的存在唯一性.pdf

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1、数学杂志Vo1．33(2013)J．ofMath．(PRC)NO．6EXISTENCEANDUNIQUENESSOFTHESOLUTIONTOINTEGRO-DIFFERENTIALEQUATIONINVOLVINGTHEGENERALIZEDP—LAPLACIANoPERAToRWITHMIXEDB0UNDARYCoNDIT10NSWEILi，DUANLi—ling，RaviP．Agarwal【1．SchoolofMathematicsandStatistics，HebeiUniversityofEconomicsandBusiness

2、，Shijiazhuang050061，China)【2．DepartmentofMathematics，TexasAgriculturalandMechanicalUniversity—KingsviUe，Texas，TX78363-8202，U．S．A．)Abstract：Onekindofintegro—diferentialequationsinvolvingthegeneralizedp-Laplacianoperatorwithmixedboundaryconditionsisstudiedinthispaper．Themet

3、hodofdecomposingtheintegro—diferentialequationtothenonlinearoperatorsareemployedandtheexistenceandunique-nessofthesolutionareobtained．Comparedtothepreviousworkonthistopic，notonlyexistencebutalsotheuniquenessofthesolutioniSobtained．Moreover，sometechniquesandresultsontheran

4、gesofmaximalmonotoneoperatorsandpseudo-monotoneoperatorsareemployedinsteadofthefiniteelementmethod，whichextendandcomplementsomepreviousworks．Keywords：maximalmonotoneoperator；pseudo—monotoneoperator；generalizedp-Laplacianoperator；Integro—diferentialequationswithmixedbounda

5、ryconditions2010MRSubjectClassification：47H05；47H09Documentcode：AArticleID：0255．7797(2013)06．1009．101IntroductionNonlinearboundaryvalueproblemsinvolvingp-Laplacianoperator—Apoccurinavarietyofphysicalphenomena．Thus，thestudyofsuchproblemsandtheirfarreachinggeneralizationsha

6、veattractedseveralmathematiciansinrecentyears．Webeganourstudyonthistopicin[1]anduntilrecently,weextendedourpreviouswork(c．f．【1-4])tothefollowingnonlinearboundaryvalueproblemwithp-Laplacianoperator(c．f．[5])：Q．Receiveddate：2012—04．25Accepteddate：2012—11-05Foundationitem：Sup

7、portedbybyNationalNaturalScienceFoundationofChina(11071053)；theNaturalScienceFoundationofHebeiProvince(A2010001482)；theKeyProjectofScienceandResearchofHebeiEducationDepartmentfZH20120801．Biography：wleiLi(1967-)，female，bornatLeting，Hebei，professor，Ph．D．，majorinnonlinearfun

8、ctionalanalysis．1010Journa1ofMathematicsVo1．33Weshowedthat(1．1)hasasolutioninL8(Q)，where而2N