Existence of positive solutions of a nonlinear fourth-order boundary value problem

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Abstract

In this paper, we study the existence of positive solutions of fourth-order boundary value problem u(4)(t) = f (t, u (t), u″(t)), t ∈ (0, 1),u (0) = u (1) = u″(0) = u″(1) = 0, where f : [0, 1] × [0, ∞) × (- ∞, 0] → [0, ∞) is continuous. The proof of our main result is based upon the Krein-Rutman theorem and the global bifurcation techniques. © 2010 Elsevier Ltd. All rights reserved.

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Ma, R., & Xu, L. (2010). Existence of positive solutions of a nonlinear fourth-order boundary value problem. Applied Mathematics Letters, 23(5), 537–543. https://doi.org/10.1016/j.aml.2010.01.007

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