Eigenvalues and symmetric positive solutions for a three-point boundary-value problem
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Date
2005-11-23
Authors
Sun, Yong-Ping
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
In this paper, we consider the second-order three-point boundary-value problem
u′′(t) + ƒ(t, u, u′, u′′) = 0, 0 ≤ t ≤ 1,
u(0) = u(1) = αu(η)
Under suitable conditions and using Schauder fixed point theorem, we prove the existence of at least one symmetric positive solution. We also study the existence of positive eigenvalues for this problem. We emphasis the highest-order derivative occurs nonlinearly in our problem.
Description
Keywords
Symmetric positive solution, Three-point boundary-value problem, Schauder fixed point theorem, Eigenvalue
Citation
Sun, Y. (2005). Eigenvalues and symmetric positive solutions for a three-point boundary-value problem. <i>Electronic Journal of Differential Equations, 2005</i>(127), pp. 1-7.