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1、一个无界区域中的奇摄动非线性椭园型系统第22卷2期1999年6月安徽师范大学(自然科学版)JournalofAnhuiNormalUniversity(NaturalScience)V01.22.No.2Jun.I999文章■号;1001-2443(1999)02O100--04ASINGULARLYPERTURBEDNONLINEARELLIPTICSYSTEMlNUNBOUNDEDDOMAINM0Jia—qi(Department0fMathematics.AnhulNormalUnlverslD",241000Wuhu,Anhui,Chi
2、na)Abstract:ThesingularlyperturbedproblemsforthenonlinearellipticsystemsinthehalfspaceRareconsidered.Undersuitableconditions,usingthecomparisontheoremtheexistenceandasymptoticbehaviorOfsolutionfortheboundaryvalueproblemsarestudied.Keywords:ellipticsystem;singularperturbation
3、;comparisontheoremCLCnumber:0l75.29Documentcode:AWeconsiderthefollowingsingularlyperturbedprobleminthehalfspace尼;{Iz>0}E2L"z—f2,1,"2.…,N,e),i一1.2,….Ⅳ.毋I,…,'一1).以=0,i一1,2.…,Ⅳ,Where(1)(Z)工:未矗+c考,∑4(z)点≥^∑,v∈R,2>0,whereeisapositiveparameter,=(I.z,…,)∈R.Theauthorstudiedacl
4、assofsingularlyper—turbedboundaryvalueproblemsfortheellipticequationsin[3"]--[6].Thispaperinvolvessingularlyper.turbedprobleminthehalfspace.Assumethat[1]thecoefficientsof工areboundedsmoothfunctionsin爱兰{f≥0)}[2】,gandtheirderivativesunitlm—thorderareboundedfunctionswithregardto
5、theirvariablesincorrespondenceranges{[H3]thereexistpositiveconstants,,suchthatexp(),i=1,2,…,N;Wenowconstructtheformalasymptoticsolutionoftheproblem(1)--(2).Thereducedproblemof(1)～(2)is,"l,如.…,N,0)=0,∈心,i—i,2,…,N.(*)Wealsoassumethat[H']thereexistsasolutionUD兰(ulD,Uzo,…,UNo)of
6、systern(*),andUI¨anditsderiratiresareboundedfunctionsin冠.I—etformalexpansionsoftheOutersolutionU;(U1,UUⅣ)fortheoriginalproblem(1)～(2)be～∑￡,,i=1.2,…,N.(3)Substituting(3)into(1),developingf~ine?equatingcoefficientsoflikepowersof~respectively.weobtain收辅日期I10驰～儿一26作者前介c羹毫琪(1937一
7、).男.教授正≥∑+22卷第2期莫嘉琪:一个无界区域中的奇摄动非线性椭园型系统101∑^.(_r,U…U2.,…+U.,0)U+F,一,1(』2)一0+i1,2,…+Ⅳ;,1+2,…,whereF,aredeterminedfunctionsofU,+r≤一1,andtheirconstructionsareomitted.Theaboveandbel0w+thevalueoftermsforthenagetivesubscriptarezero.Fromabovelinearsystem+wecansolveUlJsuccessively.F
8、orm(3),weobtaintheoutersolutionU一(UI+U,…,U)fortheoriginalproblem.Butitmayno
