Remarks on an S-shaped bifurcation curve

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Abstract

We study the non-negative solutions of the boundary value problem −Δu = λ [expαu(α + u)]; x ϵ Ω. u = 0; x ϵ ∂Ω, where α > 0, λ ⩾ 0, Ω ⊂ Rn is bounded with smooth boundary ∂Ω.

This problem arises in the theory of combustion. We study the estimates on the supremum norm of the solutions and estimates on the critical values of λ.

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Present address: Department of Mathematics, Mississippi State University, Mississippi State, MS 39762.