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On the number of positive solutions to a class of integral equations
Wang, L; Yu, WS; Zhang, L
Source PublicationCONTROL AND CYBERNETICS
2003
Volume32Issue:2Pages:383-395
SubtypeArticle
AbstractBy 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.
KeywordIntegral Equations Positive Solutions Complete Discrimination System For Polynomials Number Of Solutions
WOS HeadingsScience & Technology ; Technology
Indexed BySCI
Language英语
WOS Research AreaAutomation & Control Systems ; Computer Science
WOS SubjectAutomation & Control Systems ; Computer Science, Cybernetics
WOS IDWOS:000188398200011
Citation statistics
Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/9889
Collection09年以前成果
Affiliation1.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
Recommended Citation
GB/T 7714
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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