The author have found that differential equations provide an inexhaustible source of results and interesting and sometimes surprising phenomena. We hope that the users of this book, both students as well as teachers, will share our enthusiasm for the subject. In the book present we analyze the nonlinear coupled system with internal damping que appears na relativistic quantum mechanic is studied, questions relating to existence, uniqueness and exponential decay are studied, using approximation techniques, Galerkim’s method and appropriate estimates. Here again the Strauss technique is used by approaching each function by Lipschitzian functions and the process of passing to the limit.