Positive solutions for semipositone fourth-order two-point boundary value problems
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In this paper we investigate the existence of positive solutions of the following nonlinear semipositone fourth-order two-point boundary-value problem with second derivative.
u(4)(t) = ƒ(t, u(t), u″(t)), 0 ≤ t ≤ 1,
u′(1) = u″(1) = u‴(1) = 0, ku(0) = u‴(0),
where -6 < k < 0, ƒ ≥ -M, and M is a positive constant. Our approach relies on the Krasnosel'skii fixed point theorem.
CitationYang, D., Zhu, H., & Bai, C. (2007). Positive solutions for semipositone fourth-order two-point boundary value problems. Electronic Journal of Differential Equations, 2007(16), pp. 1-8.
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