Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second‐Order Boundary Value Problem

Chenghua Gao

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: This paper is concerned with the existence of solutions for the discrete second‐order boundary value problem Δ2u(t − 1) + λ1u(t) + g(Δu(t)) = f(t), t ∈ {1,2, …, T}, u(0) = u(T + 1) = 0, where T > 1 is an integer, f : {1, …, T} → ℝ, g : ℝ → ℝ is bounded and continuous, and λ1 is the first eigenvalue of the eigenvalue problem Δ2u(t − 1) + λu(t) = 0, t ∈ 𝕋, u(0) = u(T + 1) = 0.

Date: 2012
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https://doi.org/10.1155/2012/951251

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:951251

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