This paper is concerned with semilinear tow-point boundary value problems of the form -(p(x)u′)′ + f(x, u) = 0, a ≤ x ≤ b, α0u(a) - α1u′(a) = α, β1u′(b) + β,1u′(b) = β, αi ≥ 0, βi≥ 0, i = 0, 1, α0+α1 > 0, β0+β 1 > 0, α0+β0 > 0. Under the assumption inf fu > -λ1, where λ1 is the smallest eigenvalue of u = -(pu′)′ with the boundary conditions, unique existence theorems of solution for the continuous problem and a discretized system with not necessarily uniform nodes are given as well as error estimates. The results generalize three theorems of Lees for u″ = f(x, u), 0 ≤ x ≤ 1, u(0) = α, u(1) = β.
|ジャーナル||Japan Journal of Industrial and Applied Mathematics|
|出版ステータス||Published - 2006 10月|
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