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On the number of positive solutions to a class of integral equations
Wang, L; Yu, WS; Zhang, L
2003
发表期刊CONTROL AND CYBERNETICS
卷号32期号:2页码:383-395
文章类型Article
摘要By using the complete discrimination system for polynomials, we study the number of positive solutions in C[0,1] to the integral equation phi(x) = integral(0)(1) k(x,y) phi(n)(y)dy, where k(x,y) = phi(1)(x)phi(1)(y) + phi(2)(x)phi(2)(y),phi(i)(x) > 0, phi(i)(y) > 0,0 < x, y < 1, i = 1, 2, are continuous functions on [0, 1], n is a positive integer. We prove the following results: when n = 1, either there does not exist, or there exist infinitely many positive solutions in C[0, 1]; when n greater than or equal to 2, there exist at least 1, at most n + 1 positive solutions in C[0, 1]. Necessary and sufficient conditions are derived for the cases: 1) n = 1, there exist positive solutions; 2) n greater than or equal to 2, there exist exactly m (m epsilon {1, 2,..., n + 1}) positive solutions. Our results generalize the ones existing in the literature, and their usefulness is shown by examples.
关键词Integral Equations Positive Solutions Complete Discrimination System For Polynomials Number Of Solutions
WOS标题词Science & Technology ; Technology
收录类别SCI
语种英语
WOS研究方向Automation & Control Systems ; Computer Science
WOS类目Automation & Control Systems ; Computer Science, Cybernetics
WOS记录号WOS:000188398200011
引用统计
文献类型期刊论文
条目标识符http://ir.ia.ac.cn/handle/173211/9889
专题09年以前成果
作者单位1.Peking Univ, Dept Mech & Engn Sci, Ctr Syst & Control, Beijing 100871, Peoples R China
2.Chinese Acad Sci, Inst Automat, Lab Complex Syst & Intelligent Control, Beijing 100080, Peoples R China
3.Tsing Hua Univ, Dept Automat, Beijing 100084, Peoples R China
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Wang, L,Yu, WS,Zhang, L. On the number of positive solutions to a class of integral equations[J]. CONTROL AND CYBERNETICS,2003,32(2):383-395.
APA Wang, L,Yu, WS,&Zhang, L.(2003).On the number of positive solutions to a class of integral equations.CONTROL AND CYBERNETICS,32(2),383-395.
MLA Wang, L,et al."On the number of positive solutions to a class of integral equations".CONTROL AND CYBERNETICS 32.2(2003):383-395.
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