Iteration for a Third-Order Three-Point BVP with Sign-Changing Green's Function
نویسندگان
چکیده
منابع مشابه
Multiple Positive Solutions for a Third-order Three-point Bvp with Sign-changing Green’s Function
This article concerns the third-order three-point boundary-value problem u′′′(t) = f(t, u(t)), t ∈ [0, 1], u′(0) = u(1) = u′′(η) = 0. Although the corresponding Green’s function is sign-changing, we still obtain the existence of at least 2m−1 positive solutions for arbitrary positive integer m under suitable conditions on f .
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Hua Su School of Statistics and Mathematic, Shandong University of Finance, Jinan, Shandong 250014, China Correspondence should be addressed to Hua Su, [email protected] Received 24 October 2008; Accepted 31 January 2009 Recommended by Binggen Zhang We study the existence of positive solutions for the following nonlinear m-point boundary value problem for an increasing homeomorphism and homomorph...
متن کاملTriple Positive Solutions for a Third-order Three-point Boundary Value Problem with Sign-changing Green’s Function
In this paper, we discuss the existence of triple positive solutions for a third-order three-point boundary value problem { u′′′(t) = f(t, u(t)), t ∈ (0, 1), u′(0) = 0, u(1) = αu(η), u′′(η) = 0, where 0 < α < 1, max{ 1+2α 1+4α , 1 2−α} < η < 1. We first study the associated Green’s function and obtain some useful properties. Our main tool is the fixed point theorem due to Avery and Peterson. It...
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In this paper, we obtain the existence of positive solutions and establish two corresponding iterative schemes for the following third order three-point boundary value problem { (φ(u′′))′(t) + q(t)f(u(t)) = 0, 0 ≤ t ≤ 1, u(0) = βu(ξ), u′(1) = 0, φ(u′′(0)) = δφ(u′′(ξ)), where φ : R → R is an increasing homeomorphism and positive homomorphism. The main tool is the monotone iterative technique. An...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2014
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2014/541234