| Title:
|
Existence of multiple solutions for some functional boundary value problems (English) |
| Author:
|
Staněk, Svatoslav |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
28 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
57-65 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be the Banach space of $C^0$-functions on $\langle 0,1\rangle $ with the sup norm and $\alpha ,\beta \in X \rightarrow {R}$ be continuous increasing functionals, $\alpha (0)= \beta (0)=0$. This paper deals with the functional differential equation (1) $x^{\prime \prime \prime } (t) = Q [ x, x^\prime , x^{\prime \prime }(t)] (t)$, where $Q:{X}^2 \times {R} \rightarrow {X}$ is locally bounded continuous operator. Some theorems about the existence of two different solutions of (1) satisfying the functional boundary conditions $\alpha (x)=0=\beta (x^\prime )$, $x^{\prime \prime }(1)-x^{\prime \prime }(0)=0$ are given. The method of proof makes use of Schauder linearizatin technique and the Schauder fixed point theorem. The results are modified for 2nd order functional differential equations. (English) |
| Keyword:
|
Schauder linearization technique |
| Keyword:
|
Schauder differential equation |
| Keyword:
|
functional boundary conditions |
| Keyword:
|
boundary value problem |
| MSC:
|
34B10 |
| MSC:
|
34B15 |
| idZBL:
|
Zbl 0782.34074 |
| idMR:
|
MR1201866 |
| . |
| Date available:
|
2008-06-06T21:04:48Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107436 |
| . |
| Reference:
|
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