Multiple positive solutions for nonlinear third-order three-point boundary-value problems
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Date
2007-08-18
Authors
Guo, Li-Jun
Sun, Jian-Ping
Zhao, Ya-Hong
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
This paper concerns the nonlinear third-order three-point boundary-value problem
u‴(t) + h(t)ƒ(u(t)) = 0, t ∈ (0, 1),
u(0) = u′(0) = 0, u′(1) = αu′(η),
where 0 < η < 1 and 1 < α < 1/η. First, we establish the existence of at least three positive solutions by using the well-known Leggett-Williams fixed point theorem. And then, we prove the existence of at least 2m - 1 positive solutions for arbitrary positive integer m.
Description
Keywords
Third-order boundary value problem, Positive solution, Three-point boundary value problem, Existence, Cone, Fixed point
Citation
Guo, L. J., Sun, J. P., & Zhao, Y. H. (2007). Multiple positive solutions for nonlinear third-order three-point boundary-value problems. <i>Electronic Journal of Differential Equations, 2007</i>(112), pp. 1-7.
Rights
Attribution 4.0 International