摘要：This paper concerns the oscillation of solutions to the second-order dynamic equation ( r ( t ) x Δ ( t ) ) Δ + p ( t ) x Δ ( t ) + q ( t ) f ( x σ ( t ) ) = 0 , on a time scale T which is unbounded above. No sign conditions are imposed on r ( t ) , p ( t ) , and q ( t ) . The function f ∈ C ( R , R ) is assumed to satisfy x f ( x ) > 0 and f ′ ( x ) > 0 for x ≠ 0 . In addition, there is no need to assume certain restrictive conditions and also the both cases ∫ t 0 ∞ Δ t r ( t ) = ∞ and ∫ t 0 ∞ Δ t r ( t ) 0 , or T = { t : t = q k , k ∈ N 0 , q > 1 } and the space of harmonic numbers T = H n . Some examples illustrating the importance of our results are also included. MSC:34K11, 39A10, 39A99.
关键词：oscillation ; second order ; dynamic equations ; time scales
