Positive Solutions for Third‐Order Boundary‐Value Problems with the Integral Boundary Conditions and Dependence on the First‐Order Derivatives

Yanping Guo and Fei Yang

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: By using a fixed point theorem in a cone and the nonlocal third‐order BVP′s Green function, the existence of at least one positive solution for the third‐order boundary‐value problem with the integral boundary conditions x′′′(t) + f(t, x(t), x′(t)) = 0, t ∈ J, x(0) = 0, x′′(0) = 0, and x(1)=∫01g(t)x(t)dt is considered, where f is a nonnegative continuous function, J = [0, 1], and g ∈ L[0, 1]. The emphasis here is that f depends on the first‐order derivatives.

Date: 2013
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https://doi.org/10.1155/2013/721909

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:721909

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