1、湖南師范大學(xué)碩士學(xué)位論文一類(lèi)奇異非線(xiàn)性橢圓問(wèn)題的研究姓名：朱媛媛申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：李亦20090301ABSTRACTThisthesisfDrMaster’sdegreeco璐idersasillgularnonlinearellipticequation三三鼉_蘭莖烹：m鮑(z)亂一劬=A妒，z∈QwhereQisaboundeddomainin王P，n≥2，withC2，盧boundaryaQ，盧∈(0，1

2、)，and虬(z)，j：已(z)∈C吃，盧(豆)，a1，Q2，p∈(o，1)，AisarealparameterTheorganizationofthisthesisis嬲thefolloWing：Thech印ter1詰theintroductionWbmainlyc0璐iderthebackground，therecentdevelopmentoftheproblemand80merequiredpriorl【IlowledgeIIl

3、chapter2，weconsidersomeofthenattureoftheaboveequationwhenK；，j￡≤o(seede矗nitiononpage2)andK；—隧oweusethesupersubsolutionprinciple，ma菇malprincipleandappr0Ximationtheo巧tol【IlawtheeXi8tence，monotonicity謝threspecttoA，theboundar

4、ybeha訂ourandtheregularity0fsolutio璐Inch印ter3，、Ⅳestudythee)(istenceandthepropertyofsolutionsByusingasiIIlilarmethodwhenK1(z)，K2(z)satis如theotherconditionsKeywords：singularequation；classicals01ution；e)【istence；supersubsolu