一类偏微分包含解的存在性.pdfVIP

48 6 ( ) Vo.l 48 No. 6 2010 11 Journal of Jilin University ( Science Ed ition) Nov 2010 1, 2 2 , ( 1. , 1 0012; 2. , 1 0022) : 考虑一类偏微分包含问题: - u G (x, u). 当集值函数G (x, u)取有界紧凸值的关 于变量x 是可测的关于变量 u是闭图 时, 运用 KakutaniFan不动点定理, 证明了边值解 的存在性, 且解集是弱紧的. : 偏微分包含; 边值解; 不动点 : O175. 14 : A : 2010) 0609640 Existence of Solu tion s of a Class of Partial D ifferential Inclusions 1, 2 2 CHENG Y i , CONG Fuzhong ( 1. Institute of Mathematics, Jilin University, Changchun 1 0012, China; 2. Department of oundation, Av iation University of A ir orce, Changchun 1 0022, China) Ab stract: This paper deals w ith the boundary value problems for a class of partial d ifferential inclusions - u G (x, u). When G (x, u) takes boundedw eakly compact convex values, is m easurable about variable x, and is a closed graph about variable u, using the techn iques from theK akutan iFan fixed point theory, w e have proved the existence theorem s of boundary value solutions of the system and the solution sets are w eakly compact. Key wo rds: partial d ifferential inclusion; boundary value solution; fixed point [ 1 ], , . N N R N Euclid , ! ∀ !, ! ∀ ! R Banach X . X Pk(f )c (R)R (). p 1# p ∃ , L () 1/p !u ! =