| Title:
|
Existence of multiple positive solutions of $n{\rm th}$-order $m$-point boundary value problems (English) |
| Author:
|
Liang, Sihua |
| Author:
|
Zhang, Jihui |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
135 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
15-28 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the existence of multiple positive solutions for the boundary value problem $$ \begin{cases} (\varphi (p(t)u^{(n-1)})(t))' + a(t)f(t, u(t), u'(t), \ldots , u^{(n-2)}(t)) = 0, \quad \ 0 < t < 1, \\ u^{(i)}(0) = 0, \quad i = 0, 1, \ldots , n - 3,\\ u^{(n-2)}(0) = \sum _{i=1}^{m-2}\alpha _iu^{(n-2)}(\xi _i),\quad u^{(n-1)}(1) = 0, \end{cases} $$ where $\varphi \colon \Bbb R \rightarrow \Bbb R$ is an increasing homeomorphism and a positive homomorphism with $\varphi (0) = 0$. Using a fixed-point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. (English) |
| Keyword:
|
boundary-value problems |
| Keyword:
|
positive solutions |
| Keyword:
|
fixed-point theorem |
| Keyword:
|
cone |
| MSC:
|
34B18 |
| idZBL:
|
Zbl 1224.34068 |
| idMR:
|
MR2643352 |
| DOI:
|
10.21136/MB.2010.140679 |
| . |
| Date available:
|
2010-07-20T18:19:28Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140679 |
| . |
| Reference:
|
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