ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SECOND ORDER NONLINEAR DYNAMIC EQUATIONS

This paper is concerned with the asymptotic behavior of solutions of second order nonlinear dynamic equation (r(t)x(Delta)(t))(Delta) + p(t)phi(gamma)(x(t)) = 0, on an above-unbounded time scale T where gamma is a positive constant and where, in. addition, r and p are real-valued, rd-continuous functions on T with no explicit sign assumptions on p. Our results are established for a time scale T without assuming certain restrictive conditions on T. Several examples illustrating our results will be given.