Nonoscillation for second order sublinear dynamic equations on time scales

✍ Scribed by Lynn Erbe; Jia Baoguo; Allan Peterson

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 375 KB
• Volume: 232
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.06.039

✦ Synopsis

Consider the Emden-Fowler sublinear dynamic equation

is the usual sublinear Emden-Fowler equation which has attracted the attention of many researchers. In this paper, we allow the coefficient function p(t) to be negative for arbitrarily large values of t. We extend a nonoscillation result of Wong for the second order sublinear Emden-Fowler equation in the continuous case to the dynamic equation (0.1). As applications, we show that the sublinear difference equation

has a nonoscillatory solution, for b > 0, c > α, and the sublinear q-difference equation

x ∆∆ (t) + b(-1) n t -c x α (qt) = 0, 0 < α < 1, has a nonoscillatory solution, for t = q n ∈ T = q N 0 , q > 1, b > 0, c > 1 + α.