Open AccessExistence and Uniqueness of almost Non-Negative Periodic Solution for a Class of Generalized Sine-Gordon Equation
Author(s) -
Jianze Chen
Publication year - 2021
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2021/v36i1130419
Subject(s) - uniqueness , mathematics , class (philosophy) , fixed point theorem , banach fixed point theorem , sine gordon equation , mathematical analysis , banach space , nonlinear system , sine , fixed point , pure mathematics , computer science , physics , soliton , geometry , quantum mechanics , artificial intelligence
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.