A note on a third‐order multi‐point boundary value problem at resonance |
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Authors: | Xiaojie Lin Zengji Du Fanchao Meng |
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Affiliation: | 1. School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, Jiangsu 221116, P. R. China;2. Department of Applied Mathematics, The University of New South Wales, Sydney, NSW UNSW 2052, Australia;3. Progenitor Vocational and Technical College, Lianshui, Jiangsu 223400, P.R. China |
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Abstract: | Based on the coincidence degree theory of Mawhin, we prove some existence results for the following third‐order multi‐point boundary value problem at resonance where f: [0, 1] × R3 → R is a continuous function, 0 < ξ1 < ??? < ξm < 1, αi ∈ R, i = 1, …, m, m ≥ 1 and 0 < η1 < η2 < ??? < ηn < 1, βj ∈ R, j = 1, 2, …, n, n ≥ 2. In this paper, the dimension of the linear space Ker L (linear operator L is defined by Lx = x′′′) is equal to 2. Since all the existence results for third‐order differential equations obtained in previous papers are for the case dim Ker L = 1, our work is new. |
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Keywords: | Third‐order differential equations coincidence degree theory multi‐point boundary value problem resonance MSC (2010) 34B‐15 |
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