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研究生: 陳鳳琴
Chen Feng-Chin
論文名稱: 巴納赫空間上m-增獲算子和最大單調算子的緊緻擾動
on compact perturbations of m-accretive and maximal monotone operators in Banach spaces
指導教授: 顏啟麟
Yan, Qi-Lin
學位類別: 博士
Doctor
系所名稱: 數學系
Department of Mathematics
論文出版年: 1998
畢業學年度: 86
語文別: 中文
中文關鍵詞: m-增獲算子最大單調算子緊緻算子強增獲算子強單調算子完全連續
論文種類: 學術論文
相關次數: 點閱:243下載:3
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  • In this paper, let X be a real Banach space with dual space X* and duality mapping F. We will study the solvability of the equation Tx + Cx contains s, s belongs to X, where T:D(T)-->2^x is m-accretiveand C:D(T)-->X is either compact or is bounded with C(T+I)^(-1) beingcompact. The main method employs the Leray-Schauder degree theory in order to ensure the existence of solutions of the approximate problemsTx + Cx + (1/n)x contain s, n=1,2,.... If x_n is a solution of the previous equations and show that (1/n)x_n-->0 as n approximates to infinte, in particular {x_n} is bounded, then the range of the sum T+C is dense in X, under the assumptions of various boundary conditionsand coercivities which the operators T and C possess. Furthermore, we also find some sufficient conditions on T and C such that the range of the sum T+C is surjective on X. Some analogous results on maximal monotone operators are also discussed in this paper. In the last partof our work, we shall concern the existence of certain eigenvalue results is given by solving Tx + kCx contains 0 with respect to k is a positive number and x belongs to the boundary of G, where G is a bounded,open subset of X.

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