关于Hardy方程的研究-应用数学专业论文.docxVIP

@ @ 博士学位论文 Ⅸ)cTo恻|lL DISSERTAIION 最后我们考虑下面问蘑 j也=嗨调动等，xERN, l tI∈D各2(RⅣ)， 其中N2，K(x)是有界的连续函数且满足一些条件．D垆(R”)是一个合适的G对称 Sobolev空间．2’(。)={；；等是临界的Sobolev-Hardy指致，且0 s 82，0p豇= (下N--2)2．我们得到这个问题的G-对称解． Keywords：Sobolev，Sobolev-Hardy,紧性，(P固序列(条件)，正解，G-对称解． @ @ 博士擘往论文 DOCTOR^L埘S跖RnnON ABSTRACT This dissertation inv嚣tigates si皤：lllaf semilinear dliptie equations,whida have sin- 出coetfieient．s and critical Solx)lev-ttardy expolaelats∞critical$oboleit exponents． Ftrstlr,this paper deal with this problem {-△俨嵴佃扛扣-|训矿_2¨七(司阻I|。％、 (。)～u， I u∈H1(RⅣ)． where2‘=2Ⅳ／(N一2)istheeritiealsobmey叩n吼t，2g2．，osp乒皇垡孚￡， d(甸，知(茁)∈D(R，)．nrollgh a∞mpadn嘲锄alysis of the fmletional eorre印onding to the problems(∞，骶obtain the∞【istenoe of positive solutions for thi8 problem,mder oertaIin assumptions∞D(霉)and k(z)；and 一△“一p贵+地=k12*--2u+町lul’一2“， 吣 (螃 嚣+口(z)t‘=o on勰． where 2’=2Ⅳ／(Ⅳ一2)i8 the lilniting exponent for the embedding of日1(n)into工，(0)， 2p2‘，p卢皇i!!i壁，叩≥0 and A∈R1 alep钏旧肛lete璐，口(互)∈con)，a(￡)≥0． Through a compactness缸alysis of the functional ooⅡ唧onding to the problem(6)，we obtain the existence ofpositive solutio邯for this problem,mder different assumptions On the paralnete鹅p，A and the五lct that 0∈n or 0∈触．The main difference of problem (口)and(b)is in that the domain(botmded Or llnbo曲ded)and the boundary condition (Diriclget or Rob抽)．And we must take different method to deal the t∞problem，al∞ thjs diffelence of the咖problem indu嘲VH．y differem blow up phenomena and results． Secondly,for the foll洲ing problem relat脚l to the Cathrelli—Kolm-Nirenberg ineqllal- ities l-ai口(1=l一缸Vt‘)一Alzr啦锃=jzj一扣It‘lP一龟+刁Izf-∞lt‘f。一2u in n ‘ Ic} 【Ⅱ=0 锄砌 wherea=60，p=暑笔，d≤de≤a+l，D=丙=主‰，F=丙=ji={2N瓣- ，2口D， A and竹a舶real constants．We obtain Some existence or nonexisten∞嘲11lts for this problem． @ @ 博士学住论文 DOCTORAL DJSSERT^竹ON For nonhomogeneons Neumann boundary value problem of the type f却¨俨1。品御， {t‘0 茹∈Q， (d) L IV“l’一2．艮≈=币 ．z∈·pQ＼{o)， wherenj8 aboundeddomaininRNwith smoothboundary,0∈踟，2≤PAr，A一= dilJ(1Vu[’’2Vu)isthep-Laplacian