Opuscula Math. 37, no. 6 (2017), 839-852
Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equation
John R. Graef
Said R. Grace
Abstract. This paper discusses oscillatory and asymptotic properties of solutions of a class of third-order nonlinear neutral differential equations. Some new sufficient conditions for a solution of the equation to be either oscillatory or to converges to zero are presented. The results obtained can easily be extended to more general neutral differential equations as well as to neutral dynamic equations on time scales. Two examples are provided to illustrate the results.
Keywords: third order, neutral differential equations, asymptotic behavior, nonoscillatory, oscillatory solution.
Mathematics Subject Classification: 34K10, 34K11, 34K15, 34C10.