輔助原理在解變分不等式中的應(yīng)用.pdf

1、遼寧師范大學碩士學位論文輔助原理在解變分不等式中的應(yīng)用姓名：張黎麗申請學位級別：碩士專業(yè)：基礎(chǔ)數(shù)學指導教師：劉澤慶20020601壘咝鯉竺堂堂!竺些嬰巴塑絲壁墅!豎竺型嬰!塹型竺塑!!!磐些竺型些型墼生～11Prelimimwi8Tbm螄thispaperLlnlessotherwises眥d，letHbearealHilbertspacewithnorlnandinnerpr訕讎denotedby洲and(。，’)，％pec“VebL

2、etKe日beanoncmptyclosed。“7““她％CB(H1bethefamily。fallilon∞甲e’boundedclosedsubsetsofⅣ，RbethesetofallrealnumberslDdthcfimcaonb(，)：HH—’Rbe[10differenuableandsahsfyth。followingpropmics：fora11”，V，w∈H，(1)b(u，v)BJilcⅡmtIle6rsta‘gl

3、Ⅱll∞t(2)b(u，v)isbctdedthatis，factocrasmaconstant(3)b(u，v)一6(“，w)≤6(“，v—w)(4)b(u，V)is㈣mtbes刪ar|印m咖y0suchthatlb(u，V】≤，㈣刪ForgivensinglevaluednmppingsN：HxH_H，F(xiàn)，P，gIHjHandsetvaluedmappingsr，4：日一爭cs(H)，Weconsiderth。problemoffi

4、nding“∈日，』∈T(u)’yeA(u)suchthat90)∈Kmad(Ⅳ(Fb)，尸◇)XV—90))60，V)一6(“，90))20，forallV∈K(111)1kPr曲l∞(111)iscalledthegcncrallzedset—valuadmixedv枷oiMllinequitySome$peciIlcas∞(19IfFandParctheidemitymapping，thentheproblem(111)iscqu

5、ivaicmtofinding“∈爿，x∈r(u)，y∈彳0)suchthatg(“)∈Kand(Ⅳb，ylv—90))60，v)一6(“，90))≥0forallv∈K(1112)Theproblem(112)iscalled恤nonlinearraixcdsetvaluedvariationalmequalitiesstudiedbySalahuddin【211(z13ffT∞dA8”alnglevaluedmnppmgs，th∞t

6、heproblem(112)isequivalenttofindingⅣ∈Hsuchthatg(u1∈Kand(Ⅳ(rol爿(Ⅳ)XV—g(Ⅳ))6(“，v)一6(“，g(”))20，forallv∈K(113)Theprobkan(113)iseaUedthegen口alizednonlinearmixedvaaiationalmequality㈣IfgistheidentitymappingⅣ(丁0)彳0))=丁0)一40)，the

7、ntheproblem(113)isa乎抽“倒Ltofinding“EKsuchth疊i(7h～Au，v一Ⅳ)6(“，v)一6(“，90))≥0，forallv∈K(114)Theproblem(114)isconsideredinNoor【14]flY)Ifb(u，V)三0，theaatheproblem(I12)iseqaivalcnttofindingⅣ∈H，工∈丁(“l(fā)Y∈A(u)suchthat90)∈Kand(N(x，ylv

8、—90))≥0forallv∈K(115)1_bcproblem(114)isconsideredandsmdiedbyNcolf121Inb憾forappropriatechoicesofthemappingsN，F(xiàn)，P，g，TandA，itiseasytoSeethatthegeneralizedsetvaluednonlinearmixedvariationalinequality(1I1)includesmanykiridsof

9、variationalinequalitiesproblems，s。c【12，14，21]andthereferencestberemasspecialc∞∞WeshallneedthefollowingdolLaitionsandlemmasDdmition111Amappingg：H斗Hissaidtobestronglymonoto∞andLipschitzcontinuotIsifth∽existco眥lantsDUandd0s