| Title:
|
Boundary value problems with compatible boundary conditions (English) |
| Author:
|
Karakostas, G. L. |
| Author:
|
Palamides, P. K. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
581-592 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
If $Y$ is a subset of the space $\mathbb{R}^{n}\times {\mathbb{R}^{n}}$, we call a pair of continuous functions $U$, $V$ $Y$-compatible, if they map the space $\mathbb{R}^{n}$ into itself and satisfy $Ux\cdot Vy\ge 0$, for all $(x,y)\in Y$ with $x\cdot y\ge {0}$. (Dot denotes inner product.) In this paper a nonlinear two point boundary value problem for a second order ordinary differential $n$-dimensional system is investigated, provided the boundary conditions are given via a pair of compatible mappings. By using a truncation of the initial equation and restrictions of its domain, Brouwer’s fixed point theorem is applied to the composition of the consequent mapping with some projections and a one-parameter family of fixed points $P_{\delta }$ is obtained. Then passing to the limits as $\delta $ tends to zero the so-obtained accumulation points are solutions of the problem. (English) |
| Keyword:
|
differential equations of second order |
| Keyword:
|
two-point boundary value problems |
| MSC:
|
34B15 |
| MSC:
|
34C30 |
| MSC:
|
34C99 |
| idZBL:
|
Zbl 1081.34039 |
| idMR:
|
MR2153084 |
| . |
| Date available:
|
2009-09-24T11:25:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128004 |
| . |
| 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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