Periodic solutions for p(t)-Lienard equations with a singular nonlinearity of attractive type
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arXiv
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| Format: | Preprint |
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2025
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| author | Jebelean, Petru Mawhin, Jean Serban, Calin |
| author_facet | Jebelean, Petru Mawhin, Jean Serban, Calin |
| contents | We are concerned with the existence of $T$-periodic solutions to an equation of type $$\left (|u'(t))|^{p(t)-2} u'(t) \right )'+f(u(t))u'(t)+g(u(t))=h(t)\quad \mbox{ in }[0,T]$$ where $p:[0,T]\to(1,\infty)$ with $p(0)=p(T)$ and $h$ are continuous on $[0,T]$, $f,g$ are also continuous on $[0,\infty)$, respectively $(0,\infty)$. The mapping $g$ may have an attractive singularity (i.e. $g(x) \to +\infty$ as $x\to 0+$). Our approach relies on a continuation theorem obtained in the recent paper M. García-Huidobro, R. Manásevich, J. Mawhin and S. Tanaka, J. Differential Equations (2024), a priori estimates and method of lower and upper solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04927 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Periodic solutions for p(t)-Lienard equations with a singular nonlinearity of attractive type Jebelean, Petru Mawhin, Jean Serban, Calin Analysis of PDEs Classical Analysis and ODEs We are concerned with the existence of $T$-periodic solutions to an equation of type $$\left (|u'(t))|^{p(t)-2} u'(t) \right )'+f(u(t))u'(t)+g(u(t))=h(t)\quad \mbox{ in }[0,T]$$ where $p:[0,T]\to(1,\infty)$ with $p(0)=p(T)$ and $h$ are continuous on $[0,T]$, $f,g$ are also continuous on $[0,\infty)$, respectively $(0,\infty)$. The mapping $g$ may have an attractive singularity (i.e. $g(x) \to +\infty$ as $x\to 0+$). Our approach relies on a continuation theorem obtained in the recent paper M. García-Huidobro, R. Manásevich, J. Mawhin and S. Tanaka, J. Differential Equations (2024), a priori estimates and method of lower and upper solutions. |
| title | Periodic solutions for p(t)-Lienard equations with a singular nonlinearity of attractive type |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2506.04927 |