非梯度型弱连续映射的分歧定理及其应用
A Bifurcation Theorem of Nongradient, Weakly Continuous Maps and Applications
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摘要: 本文把M.A.Красноселъский关于紧连续映射著名的局部分歧定理推广到弱连续映射,从而可用于应用中缺乏紧性的情形.最后给出对拟线性椭圆方程Dilichlet问题的应用.Abstract: In this paper, M. A. Krasnosels'kii's local bifurcation theorem for compactly continuous mappings is extended to weakly continuous mappings. So we can surmount the difficulty of lacking compactness in application. Lastly, we apply it to Dilichlet problem of quasilinear elliptic equation.
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[1] Касноселъский М.А.,Тоnoлоuческuе Меmобы б Теорuu Нелuчеuных Инmеiралъных Урабненuu,Москва(1956) [2] Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review, 18(1976), 620-709. [3] Thomas, J.W., A bifurcation theorem for k-set contractions, Pacific J. of Math., 44, 2(1973), 749-756. [4] 陈文源,《非线性泛函分析》,甘肃人民出版社(1982) [5] 郭大钧,《非线性泛函分析》,山东科学技术出版社(1985) -
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