Knowledge Commons of Institute of Automation，CAS
On the number of positive solutions to a class of integral equations | |
Wang, L; Yu, WS; Zhang, L | |
Source Publication | CONTROL AND CYBERNETICS |
2003 | |
Volume | 32Issue:2Pages:383-395 |
Subtype | Article |
Abstract | 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. |
Keyword | Integral Equations Positive Solutions Complete Discrimination System For Polynomials Number Of Solutions |
WOS Headings | Science & Technology ; Technology |
Indexed By | SCI |
Language | 英语 |
WOS Research Area | Automation & Control Systems ; Computer Science |
WOS Subject | Automation & Control Systems ; Computer Science, Cybernetics |
WOS ID | WOS:000188398200011 |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.ia.ac.cn/handle/173211/9889 |
Collection | 09年以前成果 |
Affiliation | 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 |
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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