Johnny Henderson, Nontrivial solutions of fourth order ordinary differential equations with nonlocal three-point boundary conditions, Vol. 2022 (2022), Article ID 15, pp. 1-7

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DOI: 10.23952/cot.2022.15

Received August 15, 2022; Accepted August 31, 2022; Published October 8, 2022

Abstract. For $0 < \eta < 1$ fixed, by an application of a Krasnosel'skii-Zabreiko fixed point theorem, nontrivial solutions are established for a nonlinear fourth order differential equation, $u^{(4)}(t) + f(u(t)) = 0,$ $0 \leq t \leq 1$ , satisfying nonlocal three-point conditions $u(0) = u'(0) = u''(0) = u''(\eta) - u''(1) = 0,$ where $f:\mathbb{R} \to \mathbb{R}$ is continuous and almost linear at infinity.

How to Cite this Article:
J. Henderson, Nontrivial solutions of fourth order ordinary differential equations with nonlocal three-point boundary conditions, Commun. Optim. Theory 2022 (2022) 15.