On the Non-Negative Radial Solutions of the Two Dimensional Bratu Equation

Abstract

In this paper, we study the boundary value problem on the unit circle for the Bratu’s equation depending on the real parameter μ. From the parameter estimate, the existence of non-negative solution is set. A numerical method is suggested to justify the theoretical result. It is a combination of the adaptation of finite difference and Gauss-Seidel method allowing us to obtain a good approximation of μc, with respect to the exact theoretical method μc = λ = 5.7831859629467.