On the asymptotic behavior of the solutions of a class of second order nonlinear differential equations

In this paper, we investigate properties of the solutions of a class of second-order nonlinear differential equation such as [p(t)f(x(t))x′(t)]′ + q(t)g(x′(t))e(x(t)) = r(t)c(x(t)). We prove the theorems of monotonicity, nonoscillation and continuation of the solutions of the equation, the sufficient and necessary conditions that the solutions of the equation are bounded, and the asymptotic behavior of the solutions of the equation when t → ∞ on condition that the solutions are bounded. Also we provide the asymptotic relationship between the solutions of this equation and those of the following second-order linear differential equation: [p(t)u′(t)]′ = r(t)u(t)