| Title:
|
Solutions of a multi-point boundary value problem for higher-order differential equations at resonance. (II) (English) |
| Author:
|
Liu, Yuji |
| Author:
|
Ge, Weigao |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
209-227 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we are concerned with the existence of solutions of the following multi-point boundary value problem consisting of the higher-order differential equation \[ x^{(n)}(t)=f(t,x(t),x^{\prime }(t),\dots ,x^{(n-1)}(t))+e(t)\,,\quad 0<t<1\,,\qquad \mathrm {{(\ast )}}\] and the following multi-point boundary value conditions \begin{align*}{1}{*}{-1} x^{(i)}(0)&=0\quad \mbox{for}\quad i=0,1,\dots ,n-3\,,\\ x^{(n-1)}(0)&=\alpha x^{(n-1)}(\xi )\,,\quad x^{(n-2)}(1)=\sum _{i=1}^m\beta _ix^{(n-2)}(\eta _i)\,. \tag{**}\end{align*} Sufficient conditions for the existence of at least one solution of the BVP $(\ast )$ and $(\ast \ast )$ at resonance are established. The results obtained generalize and complement those in [13, 14]. This paper is directly motivated by Liu and Yu [J. Pure Appl. Math. 33 (4)(2002), 475–494 and Appl. Math. Comput. 136 (2003), 353–377]. (English) |
| Keyword:
|
solution |
| Keyword:
|
resonance; multi-point boundary value problem |
| Keyword:
|
higher order differential equation |
| MSC:
|
34B10 |
| MSC:
|
34B15 |
| MSC:
|
47H11 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1117.34013 |
| idMR:
|
MR2164671 |
| . |
| Date available:
|
2008-06-06T22:45:54Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107952 |
| . |
| Reference:
|
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| Reference:
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