Banach 空间中极大单调算子扰动的值域

设X为实Banach空间, T:D(T)(?)X→2X*为极大单调算子, C: D(T)(?)X→X*为有界算子(未必连续),而C(T+J)-1为紧算子．本文在上述假设条件下,通过附加一定的边界条件应用Leray-Schauder度理论研究了下述包含关系:0∈(T+C)(D(T)∩ BQ(0)),0∈(T+C)(D(T)∩ BQ(0));以及S(?)R(T+C), intS(?)intR(T+C)(其中S(?) X*);B+D(?)R(T+C),int(B+D)(?)intR(T+C)(其中 B(?)X*,D(?)X*)的可解性,得出了一些新的结论．

RANGES OF PERTURBED MAXIMAL MONOTONE OPERATORS IN BANACH SPACES

Let $X$ be a real Banach space, $T:D(T)\subset X\rightarrow 2^{X^{*}}$ be a maximal monotone operator , $C:D(T)\subset X\rightarrow X^{*}$ be bounded (but need not to be continuous) and $C(T+J)^{-1}$ be a compact operator. Under the above conditions, by adding certain boundary and making use of Leray-Schauder degree theory, in this paper we study the solvability of the following inclusions: $0\in\overline{(T+C)(D(T)\cap B_Q(0))},\hspace{1mm} 0\in(T+C)(D(T)\cap B_Q(0))$; and $S\subset\overline{R(T+C)}$, int$S$$\subset$int$ R(T+C)$ (where $S\subset X^{*}$); and $B+D\subset\overline{R(T+C)}$, int$(B+D)$$\subset$int$ {R(T+C)}$ (where $B\subset X^{*}$ and $D\subset X^{*}$). Based on this, we derive some new conclusions.