30896.非線性choquard方程解的存在性和多重性

1、非線性Choquard方程解的存在性和多重性ExistenceandmultiplicityofsolutionsfortheclassofnonlinearChoquardequation作者：周慶翡Author：圣塾Q墜Q!望g堡i指導教師：沈自飛Supervisor：墨墮旦旦型魚i專業(yè)：基礎數(shù)學Major：PureMathematics學位：墨鱟墮Degree：叢墾璺!旦!Q!曼呈墮墜塑授予單位：浙江師范大學Institute：圣

2、壘受!壘翌g墮Q!翌壘!墮望墜絲!蘭i!YMay，2014ExistenceandmultiplicityofsolutionsfortheclassofnonlinearChoquardequationABSTRACTThispaperstudiesaclassofChoquardequation一舢W(珈仁么。A(x，y)lu(y)lpz—g卜dyIur2“g(x)WhereN≥3，0肛Ⅳ：2一等P2N—p，andthefuncti

3、onsw(z)，V(z)，A(x，Y)satisfysomeassumptionsrespectivelyThispaperconsidersexistenceandmultiplicityofsolutionsoftheequationswiththefollowingtwocasesThefirstcase：whenw(z)=y(z)，A(x，Y)=n(z)Ⅱ(可)，g(x)=0，N=3，theequationIS酬z)m)u(z)

4、=n(z)上。竺圣趔蘭鏟d9Iu(z)lp一2u(z)where0肛3，生3坐P6一p，undersuitableassumptionsonthepotentialv(x)andfunctionn(z)，a(y)，theexistenceofthenontrivialsolutionwasprovedviavariafionalmethodThesecondcase：consideringwhenW(x)=v(x)1，A(x，Y)=1，