一类带有单调型算子紧扰动的半线性方程的可解性

ON THE SOLVABILITY OF SEMILINEAR EQUATIONS INVOLVING COMPACT PERTURBATIONS OF OPERAORS OF MONOTONE TYPE

本文在算子单调性和紧性假设下研究了一类半线性算子方程Ａｕ－Ｔｕ＋Ｃｕｆ的可解性，其中Ａ，Ｔ和Ｃ映实自反Ｂａｎａｃｈ空间Ｘ中的闭凸子集到它的对偶空间Ｘ＊．我们的结果扩展或改进了Ｇｕａｎ［１］最近宣布的全部结果．

in the present paper we obtain the solvability of the equation Au-Tu+Cufunder various assumptions of monotonicity and compactness on the operators A, T, and C whichmap closed convex subsets of a reflexive Banach space X into its dual space. The results extendand improve the recent ones obtained by Guan~[1].