Theoretical and numerical considerations on Bratu-type problems
DOI:
https://doi.org/10.24193/subbmath.2021.1.03Keywords:
Bratu problem, Bratu theorem, Bratu-type equation, Cauchy problem, Nicoletti problem, boundary value problem, Green function, integral equations with exponential nonlinearity, numerical aspects of Bratu's problem.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.
Mathematics Subject Classification (2010): 34B18, 47H10, 65R20, 34B27, 45G10, 35K58.
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