Article
| Title: | Positive periodic solutions to super-linear second-order ODEs (English) |
| Author: | Šremr, Jiří |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 257-275 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study the existence and uniqueness of a positive solution to the problem $$ u''=p(t)u+q(t,u)u+f(t);\quad u(0)=u(\omega ),\ u'(0)=u'(\omega ) $$ with a super-linear nonlinearity and a nontrivial forcing term $f$. To prove our main results, we combine maximum and anti-maximum principles together with the lower/upper functions method. We also show a possible physical motivation for the study of such a kind of periodic problems and we compare the results obtained with the facts well known for the corresponding autonomous case. (English) |
| Keyword: | second-order differential equation |
| Keyword: | super-linearity |
| Keyword: | positive solution |
| Keyword: | existence |
| Keyword: | uniqueness |
| MSC: | 34B18 |
| MSC: | 34C25 |
| DOI: | 10.21136/CMJ.2024.0128-23 |
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| Date available: | 2025-03-11T16:02:44Z |
| Last updated: | 2025-03-19 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152907 |
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