Abstract
The objective of this paper is to derive new Hille type and Ohriska type criteria for third-order nonlinear dynamic functional equations in the form of {a(2) (zeta )phi(alpha 2)([a(1) (zeta) phi(alpha 1) (x(Delta)(zeta))](Delta))}(Delta) + q(zeta)phi(alpha) (x(g(zeta))) = 0, on a time scale T, where Delta is the forward operator on T, alpha(1), alpha(2), alpha > 0, and g, q, a(i), i = 1,2, are positive rd-continuous functions on T, and phi(theta)(u) := vertical bar u vertical bar(theta-1) u. Our results in this paper are new and substantial for dynamic equations of the third order on arbitrary time scales. An example is included to illustrate the results.