| 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:
|
http://hdl.handle.net/10338.dmlcz/141767 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
