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Title: Solvability of a higher-order multi-point boundary value problem at resonance (English)
Author: Lin, Xiaojie
Author: Zhang, Qin
Author: Du, Zengji
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 56
Issue: 6
Year: 2011
Pages: 557-575
Summary lang: English
Category: math
Summary: Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point boundary value problem at resonance \[ \displaylines { x^{(n)}(t)=f(t, x(t), x'(t),\cdots , x^{(n-1)}(t)),\quad t\in (0,1),\cr x(0)=\sum _{i=1}^{m}\alpha _{i}x(\xi _{i}),\quad x'(0)=\cdots =x^{(n-2)}(0)=0,\quad x^{(n-1)}(1)=\sum _{j=1}^{l}\beta _{j}x^{(n-1)}(\eta _{j}),\cr } \] where $f\colon [0, 1]\times \mathbb R^n\rightarrow \mathbb R$ is a Carathéodory function, $0<\xi _{1}<\xi _{2}<\cdots <\xi _{m}<1$, $\alpha _{i}\in \mathbb R$, $i=1,2,\cdots , m$, $m\geq 2$ and $0<\eta _{1}<\cdots <\eta _{l}<1$, $\beta _{j}\in \mathbb R$, $j=1,\cdots , l$, $l\geq 1$. In this paper, two of the boundary value conditions are responsible for resonance. (English)
Keyword: multi-point boundary value problem
Keyword: coincidence degree theory
Keyword: resonance
Keyword: higher-order ODE
Keyword: degree arguments
MSC: 34B10
MSC: 34B15
MSC: 47N20
idZBL: Zbl 1249.34056
idMR: MR2886238
DOI: 10.1007/s10492-011-0033-0
Date available: 2011-12-16T15:06:31Z
Last updated: 2020-07-02
Stable URL:
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