一类带有参数的非线性算子方程的可解性  

On the Solvability of Certain Nonlinear Operator Equations with Parameters

作　　者：周海云[1] 

机构地区：[1]军械工程学院

出　　处：《河北机电学院学报》1998年第1期36-44,共9页

摘　　要：设Ｘ为自反Ｂａｎａｃｈ空间，Ｘ及其对偶Ｘ均为局部一致凸的。在对算子Ａ，Ｔ和Ｃ的弹调性和紧性的各种假设下，本文研究了方程Ａｕ＋λＪｕ－μＴｕ＋ｖＣｕ＝ｆ的可解性，其中λ，μ，ｖ〉０为固定常数，ｆ∈Ｘ给定，算子Ａ：Ｘ→Ｘ＾＊为单调的，Ｔ：Ｘ→Ｘ＊为线性紧的，Ｃ：Ｘ→Ｘ＊为全连续的或ｐ－齐次的拟单调的（ｐ〉１）所得结果扩展或改进了近期由Ｇｕａｎ，ｃｈｅｎ。Let X be a reflexive Banach space with both X and its dual X~* locally uniformly conves. The solvability of the equation au+λJu-vCu=f is studied under various assumptions of monotonicity and compactness on the operators A,T,and C.Here,λ,μ,v>0 are fixed constants and f∈X~* is fixed.The operator A:X→X~* is monotonic and T:X→X~* is linear and compact and C:X→X~* is completely continuous or homogeneous of degree p>1 and quasimonotine. Our results extend and /or improve recent results obtained by Guan,Chen,Kartsatos and Mabry,and Kesavan.

关 键 词：非线性算子理论 单调算子 巴拿赫空间 紧扰动 

分 类 号：O177.91[理学—数学]