一類帶對流項的奇異非線性橢圓型方程Dirichlet問題唯一解的漸近行為.pdf

1、煙臺大學碩士學位論文一類帶對流項的奇異非線性橢圓型方程Dirichlet問題唯一解的漸近行為姓名：馮化冰申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：張志軍20080301AbstractBytheKaramataregularvariationtheyweshowtheexactasymptoticbehaviofthesolutionnear0toaseconddernonlineardinarydifferentialproblem?

2、???(s)=g(?(s))?(s)0s∈(0a)?(0)=0Thenbyaperturbationmethodconstructingcomparisonfunctionswestudytheexactasymptoticbehavioftheuniquesolutionuλ∈C2(?)∩C(?)neartheboundarytoasingularDirichletproblem??u=b(x)g(u)λ|?u|qu0x∈?u|??=

3、0weseethattheasymptoticbehaviisindependentonλ|?uλ|q.Here?isaboundeddomainwithsmoothboundary.λ∈Rq∈[02]g∈C1((0∞)(0∞))isnonincreasingin(0∞)thereexistsγ1suchthatg?∈RVZ?1?γb∈Cα(?)fsomeα∈(01)isnonnegativeon?b|??=0.Keywds:Semil