Atypical bifurcation for periodic solutions of $ϕ$-Laplacian systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908358199476224 |
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| author | Benevieri, Pierluigi Feltrin, Guglielmo |
| author_facet | Benevieri, Pierluigi Feltrin, Guglielmo |
| contents | In this paper, we study the $T$-periodic solutions of the parameter-dependent $ϕ$-Laplacian equation \begin{equation*} (ϕ(x'))'=F(λ,t,x,x'). \end{equation*} Based on the topological degree theory, we present some atypical bifurcation results in the sense of Prodi-Ambrosetti, i.e., bifurcation of $T$-periodic solutions from $λ=0$. Finally, we propose some applications to Liénard-type equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_00325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Atypical bifurcation for periodic solutions of $ϕ$-Laplacian systems Benevieri, Pierluigi Feltrin, Guglielmo Classical Analysis and ODEs 34B15, 34C23, 34C25, 47H11, 47J05 In this paper, we study the $T$-periodic solutions of the parameter-dependent $ϕ$-Laplacian equation \begin{equation*} (ϕ(x'))'=F(λ,t,x,x'). \end{equation*} Based on the topological degree theory, we present some atypical bifurcation results in the sense of Prodi-Ambrosetti, i.e., bifurcation of $T$-periodic solutions from $λ=0$. Finally, we propose some applications to Liénard-type equations. |
| title | Atypical bifurcation for periodic solutions of $ϕ$-Laplacian systems |
| topic | Classical Analysis and ODEs 34B15, 34C23, 34C25, 47H11, 47J05 |
| url | https://arxiv.org/abs/2406.00325 |