On Solvability Theorems of Second‐Order Ordinary Differential Equations with Delay

Nai-Sher Yeh

Abstract and Applied Analysis, 2018, vol. 2018, issue 1

Abstract: For each x0 ∈ [0,2π) and k ∈ N, we obtain some existence theorems of periodic solutions to the two‐point boundary value problem u′′(x) + k2u(x − x0) + g(x, u(x − x0)) = h(x) in (0, 2π) with u(0) − u(2π) = u′(0) − u′(2π) = 0 when g : (0,2π) × R → R is a Caratheodory function which grows linearly in u as |u| → ∞, and h ∈ L1(0,2π) may satisfy a generalized Landesman‐Lazer condition (1+sign(β))∫02πh(x)v(x)dx 0gβ+(x)vx1-βdx+∫v(x)

Date: 2018
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https://doi.org/10.1155/2018/5321314

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2018:y:2018:i:1:n:5321314

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