Asymptotic Behavior of Solutions to Second-Order Nonlinear Differential Equations

In this paper the authors study the oscillation and the asymptotic behavior of solutiosn to the second-order nonlinear differential equations$[ddot x]pmX(t,x,[dot x])=0$(X_{pm})and give necessary and sufficient conditions for Equation (X_+) to have a bounded nonoscillatory solution or to be oscillatory. There are four classes of solutions to Equation (X_) with different asymptotic behavior. For each class of solution, the necessary or sufficient condition of the existence is obtained.