λ-Interval of Triple Positive Solutions for the Perturbed Gelfand Problem

Abstract

We study a two-point Boundary Value Problem depending on two parameters that represents a mathematical model arising from the combustion theory. Applying fixed point theorems for concave operators, we prove uniqueness, existence, upper, and lower bounds of positive solutions. In addition, we give an estimation for the value of λ* such that, for the parameter λ∈[λ*,λ*], there exist exactly three positive solutions. Numerical examples are presented to illustrate various cases. The results complement previous work on this problem.