On the existence of solutions for a class of fourth order differential equations

We study the existence of the homoclinic solution of a class of nonlinear fourth order ordinary differential equations, which involve particular cases of the extended Fisher–Kolmogorov and Swift–Hohenberg equations. We address the case when the source term possesses a nonlinear dependence on the first order derivative of the solution. The main result follows from an iterative method using the sequence of solutions obtained through the mountain-pass technique. In order to illustrate this method some numerical examples are shown.