带非稠密域的半线泛函微分方程解的存在性研究.pdf

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1、Æ“Ò10530ÆÒ200809010883©aÒO175.12—?a¬ÆØ©‘šÈ—•Œ‚5•¼‡©•§)•35ïÄÆž<"f²•“9Çƶ¡êƆOŽ‰ÆÆƉ;’Ä:êÆïÄ••‡©•§"˜˜c››ÔF‘šÈ—•Œ‚5•¼‡©•§)•35ïÄÆž<"f²“6¶9…¡9Çƶ¡êƆOŽ‰ÆÆƉ;’Ä:êÆïÄ••‡©•§Æž?OnÆa¬Æǃü‰ŒÆØ©JFÏ"˜˜c››ÔFStudyfortheexistenceofsolutionsofsemilinearfunctionaldifferent

2、ialequationswithnondensedomainCandidateZimingDengSupervisorandRankProfessorYuelongXiaoCollegeSchoolofMathematicsandComputationalScienceProgramPureMathematicsSpecializationPartialDifferentialEquationsDegreeMasterofScienceUniversityXiangtanUniversityDateOctober27,2011‰ŒÆÆØ©M5(²

3、µ¤¥Ø©´<3“•eÕá?1ïĤïĤJ"Ø©¥AO±I5Ú^SN§ةؕ¹?ÛÙ¦‡<½8N®²uL½>¤JŠ¬"é©ïĉѕ‡z‡<Ú8N§þ®3©¥±²(•ªI²"<¿£(²{ÆJd<«ú"Šö¶µFϵcFÆØ©‡¦^ÇÖÆØ©Šö)Æk'3!¦^ÆØ©5½§Ó¿Æ3¿•I[k'Ü€½ÅxØ©E<‡Ú>f‡§#NØ©Ú/"<ljŒÆŒ±òÆØ©ܽܩSN?k'êâ¥?1u¢§Œ±æ^K

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5、^ØÄ:½n§ïÄe‘šÈ—•Œ‚5•¼‡©•§ÐŠ¯K·Ý)•35Ú•˜5Dx(t)=Ax(t)+f(t;xt);0tT;0<<1x(t)=(t)2C:=C([r;0];E)Ú0x(t)=Ax(t)+f(t;xt);0tT;x(t)=(t)2C:=C([r;0];E)¿ü‡#(J"'…c:Riemman-Liouville©êê

6、§©êÈ©§Œ+§·Ý)§šÈ—•§ØÄ:½n"IAbstractSemilinearfunctionaldifferentialequationsarisefromthestudyofmodelsofviscoelas-ticity,electrochemistry,control,porousmedia,electromagnetic,etc.Therefore,theyhavereceivedmuchattention.Inthispaper,byusingfixedpointtheorems,westudytheexistenceanduniquenes

7、sofmildsolutionsofinitialvalueproblemsforthefollowingsemilinearfunctionaldifferentialequationswithnondensedomainDx(t)=Ax(t)+f(t;xt);0tT;0<<1x(t)=(t)2C:=C([r;0];E)and0x(t)=Ax(t)+f(t;xt);0tT;x(t)=(t)2C:=C([r;0];E)andobtain2newresults.Keywords:Riemman-Liouvillefractionalderivat

8、ive,fractionalintegral,semi-groups,mildsolutions,nondensedomain,xedpointtheorems.II8¹Á‡..............................................................IAbstract.............................................................II1˜ÙS..........................................................

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