Oscillation and Nonoscillation of Nonlinear Nonhomogeneous Differential Equations of Third Order

Abstract

This chapter is concerned with the study of oscillatory and asymptotic behaviour of nonoscillatory solutions of nonhomogeneous third-order differential equations of the form

$$x^{\prime\prime\prime} + a(t) x^{\prime\prime} + b(t)x^{\prime} + c(t) x = f \bigl(t,x,x^{\prime},x^{\prime\prime}\bigr), $$

where a, b and c∈C([σ,∞),R) and f:[σ,∞)×R ³→R, σ∈R. z-type oscillation criteria has been used in this chapter to study the nonoscillation of solutions of the considered equation. As an application, some sufficient conditions have been given for the nonoscillation of different mathematical models in Engineering.