Positive Solutions for Neumann Boundary Value Problems of Second‐Order Impulsive Differential Equations in Banach Spaces

Xiaoya Liu and Yongxiang Li

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

Abstract: The existence of positive solutions for Neumann boundary value problem of second‐order impulsive differential equations −u″(t) + Mu(t) = f(t, u(t), t ∈ J, t ≠ tk, -Δu′|t=tk=Ik(u(tk)), k = 1,2, …, m, u′(0) = u′(1) = θ, in an ordered Banach space E was discussed by employing the fixed point index theory of condensing mapping, where M > 0 is a constant, J = [0,1], f ∈ C(J × K, K), Ik ∈ C(K, K), k = 1,2, …, m, and K is the cone of positive elements in E. Moreover, an application is given to illustrate the main result.

Date: 2012
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https://doi.org/10.1155/2012/401923

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:401923

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