Existence of Running Solutions in a Relativistic Tricomi’s Equation Using Perturbation Theory

Abstract

We use perturbation methods to establish the existence of a second kind periodic solution (running solution) of a nonlinear Tricomi’s equation type under relativistic effects. First, we estimate conditions for the existence of either an equilibrium point or a second-kind periodic solution through the average method, where we assumed the nonlinear part as a positive perturbation. Then, we use the Melnikov function to estimate conditions for the existence of running solutions, considering the persistence of the homoclinic orbits associated with the conservative equation.