涉及松弛Lipschitz和松弛單調(diào)映射的廣義非線性集值擬變分包含.pdf

1、遼寧師范大學(xué)碩士學(xué)位論文涉及松弛Lipschitz和松弛單調(diào)映射的廣義非線性集值擬變分包含姓名：金麗申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)（數(shù)學(xué)）指導(dǎo)教師：劉澤慶200210170encvslized邶蚰i嘣m硼d伯II叫q‘蚓’aliad蛆lincltmmns曲咖蝻蜷拈l刪“p酬乜endJdaxedm∞呻螄m叩piq弘一‘，y)：Ⅳ啼2月isam騏酬蝴瑚啦g，and(g一刪b)=gG)一嘶)衙eachx∈HLetKbeAnonemptycl

2、osedconvvgsubsetofHand攻betheprojectionofHontoKNowweconsiderthefollowingproblcmFind工EⅣ，”∈MrWe。斯and：ETxstraBthatQ一—lX并)∈dom(一(，J))and0∈Ⅳ0，w=)』“g—mXxlx)(11)Thewoblem(1I)iscalledthe鬻me珊lia礬nonlinearmuitivaluedquasivariationa

3、l如cl峭iofIwhichhaspotential印pIic撕m鴣inmechanicsphysicsdifferentiale零珥b吼s，pureandappliedsciences(s∞【31)(I)IfⅣ“j，，2)=』“J，以一ky)=一G)’m0)=0forallxyz∈Ⅳ，thentheixoblm(11)isequivalentto在I蜘JeⅣ，缸乍^矗andw∈SxsuchthatgixJ∈dom似Jand0∈Ⅳ0，w

4、)一(gO))(12)The弘曲蛔n(12)iscalledthegmmflizcdramlineⅢmultivaluedvaristiona]inclusion。whichincludesthesecla$s醑ofvariationalmeq喇esandvariationalinclusionsinf11，【4】一吼【8HI∞鵝specialcgses(Ⅱ)if刪b)=ON(xy，z)=J一)‘彳kJ，)=』0)forallxyz∈何

5、，thentheprohtem(11)is伽uivalcmttOfugling善EH，“∈^扛andwef汶suchOmtg(x)edom(A)and0EH—W一(g(工J)，(13)whichiscalledthegenearalizednonlinearvariationalinclusion(Ⅲ)IftqxyO=xyforallxyz∈HandM，s：H4Ⅳ辯sin翻evaluedm印伽ngs’thenthe刪啪(1，1)gG)E

6、dom0(’工))andisequivalenttOfindingx∈Hsuch曲眥0e^fG)一sG)爿“g一掰k)’喜)，(14)whichiscalledthegetamdizednonlineariqmchquasivariationalinclusionsLnmxlucvdandstudiedbyHuang嘲、Itiswellknownthatthesubdi㈣ofaproperconvexlowersen吐con6ln蛐ft

7、m甜onis8maximalmonotonemapping(IV)If—嗄工)；0foreach算∈H，A=a織where妒：H《一∞，佃】isaproperc刪v％lowersemicontimamsftlnctiml蛐Ⅳ鋤da口deloReSthesubdiffemntialof缸略ti∞妒withg(H)ndomD礦≠g，tiara吐磚肭lem(11)isequi柚aattofmdinsxEH，甜E脅，’I’ESxandzEAsu