Remark on a sufficient condition for multiplicity in a model in chemical reactor theory

摘要

We consider the model −u″ = λ(σ − u)exp{−k(l+u)}; x ϵ (0, 1) u(0) = 0 = u(1) which arises in chemical reactor theory. Here λ, σ, and k are positive constants. It is known that if there exists an α ϵ (0, σ) such that H(α) =∫0αf(s) ds − (α2)f(α )< 0 then there exists a range of λ for which there exists at least three nonnegative solutions, and using numerical evaluation it was conjectured that such values of α exist. In this paper we give an analytical proof of this conjecture.