Ranges of densely defined generalized pseudomonotone perturbations of maximal monotone operators

被引:17
作者
Guan, Z
Kartsatos, AG [1 ]
Skrypnik, IV
机构
[1] Univ S Florida, Dept Math, Tampa, FL 33620 USA
[2] Univ Wisconsin, Dept Math, Eau Claire, WI 54702 USA
[3] Inst Appl Math & Mech, UA-340114 Donetsk, Ukraine
关键词
ranges of sums; maximal monotone operator; generalized pseudomonotone perturbation; generalized (S+)-condition; degree theory;
D O I
10.1016/S0022-0396(02)00066-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let X be a real reflexive Banach space and A:X-->2(X*) be maximal monotone. Let B : X-->2(X*) be quasibounded, finitely continuous and generalized pseudomonotone with X' subset of D(B), where X' is a dense subspace of X such that X' boolean AND D(A) not equal 0. Let S subset of X*. Conditions are given under which S subset of <(R(A + B))over bar> and int S subset of int R(A + B). Results of Browder concerning everywhere defined continuous and bounded operators B are improved. Extensions of this theory are also given using the degree theory of the last two authors concerning densely defined perturbations of nonlinear maximal monotone operators which satisfy a generalized (S+)-condition. Applications of this extended theory are given involving nonlinear parabolic problems on cylindrical domains. (C) 2002 Elsevier Science (USA). All rights reserved.
引用
收藏
页码:332 / 351
页数:20
相关论文
共 27 条
[21]  
KARTSATOS AG, IN PRESS INVARIANCE
[22]  
Kartsatos AG, 1999, ADV DIFFERENTIAL EQU, V4, P413
[23]  
Pascali D., 1978, SBURLAN NONLINEAR MA
[24]   ON MAXIMALITY OF SUMS OF NONLINEAR MONOTONE OPERATORS [J].
ROCKAFELLAR, RT .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 149 (01) :75-+
[25]  
SIMONS J, 1998, LECT NOTES MATH, V1693
[26]  
Skrypnik I., 1994, TRANSLATIONS MATH MO, V139
[27]  
Zeidler E., 2013, NONLINEAR FUNCTIONAL