Convergence of solutions of certain fourth-order nonlinear differential equations (Q925392)

This paper establishes sufficient conditions for the existence of convergence of solutions for the class of fourth-order nonlinear differential equations of the form \[ x^{(4)} + a{x}''' + f(x,{x}'){x}'' + g({x}') + h(x) = p(t), \] where \(a\) is a positive constant, the functions \(f\), \(g\), \(h\) and \(p\) are continuous. By introducing a complete Lyapunov function, a theorem is proved on the subject.