| Title:
|
Positivity of Green's matrix of nonlocal boundary value problems (English) |
| Author:
|
Domoshnitsky, Alexander |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
139 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
621-638 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We propose an approach for studying positivity of Green's operators of a nonlocal boundary value problem for the system of $n$ linear functional differential equations with the boundary conditions $n_{i}x_{i}-\sum \nolimits _{j=1}^{n}m_{ij}x_{j}=\beta _{i}$, $i=1,\dots ,n$, where $n_{i}$ and $m_{ij}$ are linear bounded “local” and “nonlocal“ functionals, respectively, from the space of absolutely continuous functions. For instance, $n_{i}x_{i}=x_{i}(\omega )$ or $n_{i}x_{i}=x_{i}(0)-x_{i}(\omega )$ and $m_{ij}x_{j}=\int _{0}^{\omega }k(s)x_{j}(s) {\rm d} s +\sum \nolimits _{r=1}^{n_{ij}}c_{ijr}x_{j}(t_{ijr})$ can be considered. It is demonstrated that the positivity of Green's operator of nonlocal problem follows from the positivity of Green's operator for auxiliary “local” problem which consists of a “close” equation and the local conditions $n_{i}x_{i}=\alpha _{i}$, $i=1,\dots ,n.$ (English) |
| Keyword:
|
functional differential equation |
| Keyword:
|
nonlocal boundary value problem |
| Keyword:
|
positivity of Green's operator |
| Keyword:
|
fundamental matrix |
| Keyword:
|
differential inequalities |
| MSC:
|
34B27 |
| MSC:
|
34B40 |
| MSC:
|
34K06 |
| MSC:
|
34K10 |
| idZBL:
|
Zbl 06433686 |
| idMR:
|
MR3306852 |
| DOI:
|
10.21136/MB.2014.144139 |
| . |
| Date available:
|
2015-02-04T09:19:50Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144139 |
| . |
| Reference:
|
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