Theoretical and numerical considerations on Bratu-type problems

Abstract

In this paper we present an heuristic introduction to Bratu problem
and we give some variants of Bratu's theorem (G. Bratu, Sur les equations
integrales non lineaires, Bulletin Soc. Math. France, 42(1914), 113-142). Using the positivity of Green's function, the monotone iterations technique and the contraction principle, some generalizations of Bratu's result are also given. Numerical aspects are also considered.