A new topological degree theory for perturbations of the sum of two maximal monotone operators |
| |
Authors: | Dhruba R Adhikari |
| |
Institution: | a Department of Sciences and Mathematics, Mississippi University for Women, 1100 College Street, MUW-100, Columbus, MS 39701, USAb Department of Mathematics, University of South Florida, Tampa, FL 33620-5700, USA |
| |
Abstract: | Let X be an infinite dimensional real reflexive Banach space with dual space X∗ and G⊂X, open and bounded. Assume that X and X∗ are locally uniformly convex. Let T:X⊃D(T)→2X∗ be maximal monotone and strongly quasibounded, S:X⊃D(S)→X∗ maximal monotone, and C:X⊃D(C)→X∗ strongly quasibounded w.r.t. S and such that it satisfies a generalized (S+)-condition w.r.t. S. Assume that D(S)=L⊂D(T)∩D(C), where L is a dense subspace of X, and 0∈T(0),S(0)=0. A new topological degree theory is introduced for the sum T+S+C, with degree mapping d(T+S+C,G,0). The reason for this development is the creation of a useful tool for the study of a class of time-dependent problems involving three operators. This degree theory is based on a degree theory that was recently developed by Kartsatos and Skrypnik just for the single-valued sum S+C, as above. |
| |
Keywords: | Primary 47H14 47H07 47H11 |
本文献已被 ScienceDirect 等数据库收录! |
|