- Tytuł:
- On the number of positive solutions to a class of integral equations
- Autorzy:
-
Wang, L.
Yu, W.
Zhang, L. - Powiązania:
- https://bibliotekanauki.pl/articles/206271.pdf
- Data publikacji:
- 2003
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
równanie całkowe
rozwiązanie dodatnie
integral equations
positive solutions
complete discrimination system for polynomials
number of solutions - Opis:
- 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[...] k(x,y)phi^n(y)dy, where k(x,y) = phi1(x)phi1(y)+phi2(x)phi2(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 [is greater than or equal] 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 [is greater than or equal to] 2, there exist exactly m (m belongs to {1,2,..., n + 1}) positive solutions. Our results generalize the ones existing in the literature, and their usefulness is shown by examples.
- Źródło:
-
Control and Cybernetics; 2003, 32, 2; 383-395
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł