Schr？dinger-Hartree方程爆破解的存在性-论文.pdf

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1、第37卷第2期南京师大学报(自然科学版)V01．37NO．22014年6月JOURNALOFNANJINGNORMALUNIVERSITY(NaturalScienceEdition)June，2014Blow-upSolutionstotheSchriidinger-HartreeEquationTangXingdong(SchoolofMa~ematicalSciences，NamingNormalUniversity，Nanjing210023，China)Abstract：Inthispaper，westudytheblow

2、—upsolutionsforthenonlinearSchrsdinger—Hartreeequation，wegiveanothercharacterizationoftheblow—upsolutions．Keywords：Sch~dingerequation，blow-up，variationalcharacterizationCLCnumber：0175．29Documentcode：AArticleID：1001-4616(2014)02-0033-06Schriidinger-Hartree方程爆破解的存在性唐兴栋(南

3、京师范大学数学科学学院，江苏南京210023)[摘要]本文研究了一类SchrOdinger．Hartree方程，给出了爆破解的另外一种刻画．[关键词]薛定谔方程，爆破，变分刻画ThispaperisdevotedtothestudyoftheSchr0dinger-Poissonsystemri0u+Au=PIul～，(，)∈R+xR，{AP=I“ip，(1)【u(0，)=／L0()，whereu：R+xRI—c，n≥3and1+号印<1+．Onecanverifythat(1)isessentiallyequivalenttoth

4、efollowingSchrtidinger-Hartreeequationi0u+Au=一(1·I2-dXIMI)Iul一，(t，)∈R+xR，u(0，)=U0()(2)Miao．XuandZhaolJestablishedglobalexistenceforsolutionswithfiniteenergyinthecaseofd=6andP2．GenevandVenkov[引establishedtheexistenceofsolitarywavesolutionsandlocalexistencewithinitialdat

5、a．Inthispaper，followingIbrahim，MasmoudiandNakanishi’Sideas，wecharacterizethegroundstateofintermsofsomeconstrainedminimizationproblem，what’Smore，weobtainsomeblow—upcriterionfortheSchrtidinger—Hartreeequation(2)．NotationThroughoutthispaper，wedenotetheLebesgueLq-spaceonRb

6、yL(R)withBorlnl0，1≤g<∞．WeemployinhomogeneousSobolevspaceH(R)，whichisdefinedasH1(R)={∈t2(R)：I1M}ll=llUll+llVM0．WeusethenotationX～YwheneverX

7、atorLacling。nanyfuncti。na1．，(R)I---~R，by()=击．，(咖：．一2)I．ThenthescalingderivativeofJs(咖)isReceiveddate：2013—03—06．Foundationitem：SupposedbytheNationalNaturalScienceFoundationofChina(10871096)，theProjectofGraduateEducationInnovationofJiangsuProvince(CXLX13_367)．Correspond

8、ingauthor：TangXingdong，Ph．D，majoredinnonlinearfunctionalanalysis．E—mail：xdtang202@gmail．com一33—南京师大学报(自然科学版)第37卷第2期(2