On the number of positive solutions of systems of nonlinear dynamic equations on time scales

✍ Scribed by Hong-Rui Sun; Wan-Tong Li

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 180 KB
• Volume: 219
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.07.007

✦ Synopsis

In this paper we consider the following n-dimensional second-order nonlinear system on time scales

f i (u)/ u . Define i 0 = number of zeros in the set {f 0 , f ∞ } and i ∞ = number of infinities in the set {f 0 , f ∞ }. By using fixed point index theory, we show that:

(i) if i 0 = 1 or 2, then there exist 0 > 0 such that the system has i 0 positive solution(s) for > 0 ;

(ii) if i ∞ = 1 or 2, then there exist 0 > 0 such that the system has i 0 positive solution(s) for 0 < < 0 ;

(iii) if i 0 = 0 or i ∞ = 0, then the system has no positive solution for sufficiently large or small > 0, respectively.