Critical Points Theory and the Forced Pendulum Equation

In this work we use variational methods to show the existence of a weak solution to the problem that is an Ordinary Differential Equation of the type u`` (t)+G'' (u(t))= f(t). In the first chapter our goal is to demonstrate the deformation theorem and some abstract theorems which will be of great importance in the development of the next chapters. In the second chapter our goal is to use variational methods to show the existence of T -periodic solutions to the equation u'''' (t) +G''(u(t)) = f(t). In particular if we consider G(u) = -cosu we obtain the forced pendulum equation u'''' (t) +sen(u(t)) = f(t).