Abstract: An
existence theorem is proven to investigate sufficient conditions of a nontrivial
solution, for a general nonlinear fourth order ordinary differential equation
provided
that and
are
bounded, and satisfy
certain sufficient conditions. Then, there exists a bounded space for state
variables, in which the equation has an answer. For this purpose we use the
existence of the Green’s function and Schauder’s fixed point theorem. The
condition is applied to a nonlinear two degrees of freedom vibrating system, and
Bouasse-Sarda regulator mechanical system.
Keywords and phrases: periodicity conditions, fixed point theorem, fourth order systems, Bouasse-Sarda regulator.
