| Title:
|
Resonance and multiplicity in periodic boundary value problems with singularity (English) |
| Author:
|
Rachůnková, Irena |
| Author:
|
Tvrdý, Milan |
| Author:
|
Vrkoč, Ivo |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
45-70 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the boundary value problem \[ u^{\prime \prime }+k\,u=g(u)+e(t),\quad u(0)=u(2\pi ),\,\,u^{\prime }(0)=u^{\prime }(2\pi ), \] where $k\in \mathbb{R}$, $g\:I\mapsto \mathbb{R}$ is continuous, $e\in \mathbb{L}J$ and $\lim _{x\rightarrow 0+}\int _x^1g(s)\,\hspace{0.56905pt}\text{d}s=\infty .$ In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems. (English) |
| Keyword:
|
second order nonlinear ordinary differential equation |
| Keyword:
|
periodic problem |
| Keyword:
|
lower and upper functions |
| MSC:
|
34B15 |
| MSC:
|
34C25 |
| idZBL:
|
Zbl 1023.34015 |
| idMR:
|
MR1973424 |
| DOI:
|
10.21136/MB.2003.133937 |
| . |
| Date available:
|
2009-09-24T22:06:52Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133937 |
| . |
| Reference:
|
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| Reference:
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