Existence and Uniqueness of almost Non-Negative Periodic Solution for a Class of Generalized Sine-Gordon Equation

In this paper, we have proved the existence and uniqueness of almost non-negative periodic solution to a class of generalized Sine-Gordon equation. The main method used is the maximum principle of telegraph equation established by Mawhin, Ortega and Robles-Pérez. The main technique used is Banach fixed point theorem in functional analysis. The conclusion is that when the coefficients and nonlinear terms of the equation meet certain conditions, the generalized equation has a unique almost non-negative periodic solution. Generalized the results of Mawhin, Ortega and Robles-Pérez.