Convergence of solutions of some fourth order nonlinear differential equations

In this paper, we prove results on the convergence of solutions of a general fourth-order non-linear differential equations of the formequation(0.1)xiv+ψ(x‴)+f(x″)+g(x′)+h(x)=p(t,x,x′,x″,x‴)xiv+ψ(x‴)+f(x″)+g(x′)+h(x)=p(t,x,x′,x″,x‴)in which ψ(x‴)ψ(x‴), f(x″)f(x″), g(x′)g(x′), and h(x)h(x) are continuous in their respective arguments. While using the Lyapunov method, the restriction of the incrementary ratio of h(x)h(x) in the closed sub-interval of the Routh–Hurwitz interval is used. The results generalize and give fourth-order extensions of earlier results.