Abstract
We study the non-negative solutions of the boundary value problem −Δu = λ [ exp αu (α + u) ]; x ϵ Ω. u = 0; x ϵ ∂Ω, where α > 0, λ ⩾ 0, Ω ⊂ R n 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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