| Title:
|
On the existence of one-signed periodic solutions of some differential equations of second order (English) |
| Author:
|
Ligęza, Jan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
119-134 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the existence of one-signed periodic solutions of the equations \begin{align} & x^{\prime \prime } (t) - a^2(t) x(t) + \mu f(t, x(t), x^{\prime }(t)) = 0, & x^{\prime \prime }(t) + a^2(t) x(t) = \mu f(t, x(t), x^{\prime }(t)), \end{align} where $ \mu > 0$, $a: (-\infty , +\infty ) \rightarrow (0, \infty ) $ is continuous and 1-periodic, $f$ is a continuous and 1-periodic in the first variable and may take values of different signs. The Krasnosielski fixed point theorem on cone is used. (English) |
| Keyword:
|
positive solutions |
| Keyword:
|
boundary value problems |
| Keyword:
|
cone |
| Keyword:
|
fixed point theorem |
| MSC:
|
34B10 |
| MSC:
|
34B15 |
| MSC:
|
34B18 |
| MSC:
|
34C25 |
| MSC:
|
34G20 |
| MSC:
|
34K10 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 05184554 |
| idMR:
|
MR2321304 |
| . |
| Date available:
|
2009-08-21T07:05:44Z |
| Last updated:
|
2013-09-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133447 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Agarwal R. P., O’Regan D.: Infinite Interval Problems For Differential, Difference, Integral Equations. : Kluwer Acad. Publishers, Dordrecht, Boston, London., 2001. MR 1845855 |
| Reference:
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| Reference:
|
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| Reference:
|
[6] Santanilla J.: Nonnegative solutions to boundary value problems for nonlinear first and second order ordinary differential equations.J. Math. Annal. Appl. 126 (1987), 397–408. Zbl 0629.34017, MR 0900756, 10.1016/0022-247X(87)90049-7 |
| Reference:
|
[7] Torres P. J.: Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem.J. Diff. Eq. 190 (2003), 643–662. MR 1970045, 10.1016/S0022-0396(02)00152-3 |
| Reference:
|
[8] Zima M.: Positive Operators in Banach Spaces, Their Applications. : Wydawnictwo Uniwersytetu Rzeszowskiego, Rzeszów.2005. MR 2493071 |
| . |
