Solvability of nth-order Lipschitz equations with nonlinear three-point boundary conditions

Title
Solvability of nth-order Lipschitz equations with nonlinear three-point boundary conditions
Author(s)
Minghe Pei[Minghe Pei]장성각
Keywords
POSITIVE SOLUTIONS; DIFFERENTIAL-EQUATIONS; UNIQUENESS THEOREMS; INTERVAL LENGTHS; EXISTENCE; 2-POINT
Issue Date
201411
Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
Citation
BOUNDARY VALUE PROBLEMS
Abstract
In this paper, we investigate the solvability of nth-order Lipschitz equations y((n)) = f (x, y, y',..., y((n-1))), x1 <= x <= x(3), with nonlinear three-point boundary conditions of the form k(y(x(2)), y'(x(2)),..., y((n-1))(x(2)); y(x(1)), y' (x(1)),..., y((n-1))(x(1))) = 0, g(i)(y((i))(x(2)), y((i+1))(x(2)),..., y((n-1))(x(2))) = 0, i = 0,1,..., n-3, h(y(x(2)), y'(x(2)),..., y((n-1))(x(2)); y(x(3)), y'(x(3)),..., y((n-1))(x(3))) = 0, where n >= 3, x(1) <= x(2) <= x(3). By using the matching technique together with set-valued function theory, the existence and uniqueness of solutions for the problems are obtained. Meanwhile, as an application of our results, an example is given.
URI
http://hdl.handle.net/YU.REPOSITORY/30467http://dx.doi.org/10.1186/s13661-014-0239-7
ISSN
1687-2770
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이과대학 > 수학과 > Articles
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