Geodesic
On the Non-Negative Radial Solutions of the Two Dimensional Bratu Equation
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 2, p. 275 .

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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 $\mu_c$, with respect to the exact theoretical method $\mu_c=\lambda=5.7831859629467$.
Classification : 35J25 35J60
Keywords: non-linear eigenvalue problem, finite difference method, Gauss-Seidel method 
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     title = {On the {Non-Negative} {Radial} {Solutions} of the {Two} {Dimensional} {Bratu} {Equation}},
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Mbe Koua Christophe Ndjatchi; Panayotis Vyridis; Juan Martínez; J. Juan Rosales. On the Non-Negative Radial Solutions of the Two Dimensional Bratu Equation. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 2, p. 275 . http://geodesic.mathdoc.fr/item/KJM_2021_45_2_a9/