Oscillation of second-order nonlinear neutral delay dynamic equations on time scales

• Authors: S. H. Saker
• Venue: Journal of Computational and Applied Mathematics
• Year: 2006

In this paper, some sufficient conditions for oscillation of the second-order nonlinear neutral delay dynamic equation (r(t)([y(t)+p(t)y(t-@t)]^@D)^@c)^@D+f(t,y(t-@d))=0,on a time scale T are established; here @c=1 is an odd positive integer with r(t) and p(t) are rd-continuous functions defined on T. Our results as a special case when T=R and T=N, involve and improve some well-known oscillation results for second-order neutral delay differential and difference equations. When T=hN and T=q^N={t:t=q^k,k@?N,q1}, i.e., for generalized neutral delay difference and q-neutral delay difference equations our results are essentially new and also can be applied on different types of time scales, e.g., T=N^2={t^2:t@?N} and T=T"n={t"n:n@?N"0} where {t"n} is the set of harmonic numbers. Some examples illustrating our main results are given.