| Title:
|
Unique solvability of a linear problem with perturbed periodic boundary values (English) |
| Author:
|
Mehri, Bahman |
| Author:
|
Nojumi, Mohammad H. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
351-362 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the problem with perturbed periodic boundary values \[ \left\rbrace \begin{array}{ll}y^{\prime \prime \prime }(x) + a_2(x) y^{\prime \prime }(x) + a_1(x) y^{\prime }(x) + a_0(x) y(x) = f(x) , y^{(i)}(T) = c y^{(i)}(0), \ i = 0, 1, 2; \ 0 < c < 1 \end{array}\right.\] with $a_2, a_1, a_0 \in C[0,T]$ for some arbitrary positive real number $T$, by transforming the problem into an integral equation with the aid of a piecewise polynomial and utilizing the Fredholm alternative theorem to obtain a condition on the uniform norms of the coefficients $a_2$, $a_1$ and $a_0$ which guarantees unique solvability of the problem. Besides having theoretical value, this problem has also important applications since decay is a phenomenon that all physical signals and quantities (amplitude, velocity, acceleration, curvature, etc.) experience. (English) |
| Keyword:
|
Ordinary differential equations |
| Keyword:
|
integral equations |
| Keyword:
|
periodic boundary value problems |
| MSC:
|
34B05 |
| MSC:
|
34B15 |
| MSC:
|
34C10 |
| MSC:
|
45B05 |
| idZBL:
|
Zbl 0955.34007 |
| idMR:
|
MR1692528 |
| . |
| Date available:
|
2009-09-24T10:23:16Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127493 |
| . |
| Reference:
|
[1] H. Brezis: Analyse Fonctionnelle, Théorie et Applications.Masson, Paris, 1983. Zbl 0511.46001, MR 0697382 |
| Reference:
|
[2] R. Brown: A Topological Introduction to Nonlinear Analysis.Birkhäuser, Boston, 1993. Zbl 0794.47034, MR 1232418 |
| Reference:
|
[3] J. A. Cochran: Analysis of Linear Integral Equations.McGraw Hill, New York, 1972. Zbl 0233.45002, MR 0447991 |
| Reference:
|
[4] R. Kress: Linear Integral Equations.Springer-Verlag, New York, 1989. Zbl 0671.45001, MR 1007594 |
| Reference:
|
[5] M. Reed, and B. Simon: Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis.Academic Press, Orlando, Florida, 1980. MR 0751959 |
| . |
