Existence and relaxation results for nonlinear second-order multivalued boundary value problems in RN

被引:25
作者
Halidias, N [1 ]
Papageorgiou, NS [1 ]
机构
[1] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece
关键词
maximal monotone map; compact operator; compact embedding; Leary-Schauder alternative theorem; continuous selector; extremal solution; relaxation theorem; Aumann's selection theorem;
D O I
10.1006/jdeq.1998.3439
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we study second order differential inclusions with nonlinear boundary conditions. Our formulation is general and incorporates as special cases well-known problems such as the Dirichlet (Picard), Neumann, and periodic problems. We prove existence theorems under various sets of hypotheses for both the convex and nonconvex problems. Also we show the existence of extremal solutions and that the extremal solutions are dense in the solutions of the convex problem for the W-1,W-2 (T, R-N)-norm (strong relaxation theorem). Finally we examine the Dirichlet problem when the multivalued right-hand side does not depend on the derivative of.x and satisfies a general growth hypothesis and a sign-type condition. For this problem we prove existence results and a relaxation theorem. (C) 1998 Academic Press.
引用
收藏
页码:123 / 154
页数:32
相关论文
共 29 条
[1]  
Attouch H., 1984, Applicable Mathematics Series
[2]  
Benamara M., 1975, THESIS U GRENOBLE
[3]   EXTENSIONS AND SELECTIONS OF MAPS WITH DECOMPOSABLE VALUES [J].
BRESSAN, A ;
COLOMBO, G .
STUDIA MATHEMATICA, 1988, 90 (01) :69-86
[4]  
Brezis H., 1983, ANAL FONCTIONELLE
[5]   ON CONTINUOUS APPROXIMATIONS FOR MULTIFUNCTIONS [J].
DEBLASI, FS ;
MYJAK, J .
PACIFIC JOURNAL OF MATHEMATICS, 1986, 123 (01) :9-31
[6]   NON-CONVEX-VALUED DIFFERENTIAL-INCLUSIONS IN BANACH-SPACES [J].
DEBLASI, FS ;
PIANIGIANI, G .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 157 (02) :469-494
[7]   TOPOLOGICAL PROPERTIES OF NONCONVEX DIFFERENTIAL-INCLUSIONS [J].
DEBLASI, FS ;
PIANIGIANI, G .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1993, 20 (07) :871-894
[8]  
DEBLASI FS, 1992, ANN POL MATH, V57, P133
[9]  
ERBE L, 1990, ANN POL MATH, V56, P195
[10]   BOUNDARY-VALUE-PROBLEMS FOR 2ND-ORDER DIFFERENTIAL-SYSTEMS [J].
ERBE, LH ;
PALAMIDES, PK .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1987, 127 (01) :80-92