Monotonicity of the period and positive periodic solutions of a quasilinear equation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912818961317888 |
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| author | Dolbeault, Jean García-Huidobro, Marta Manásevich, Raúl |
| author_facet | Dolbeault, Jean García-Huidobro, Marta Manásevich, Raúl |
| contents | We investigate the monotonicity of the minimal period of periodic solutions of quasilinear differential equations involving the $p$-Laplace operator. First, the monotonicity of the period is obtained as a function of a Hamiltonian energy in two cases. We extend to $p\ge2$ classical results due to Chow-Wang and Chicone for $p=2$. Then we consider a differential equation associated with a fundamental interpolation inequality in Sobolev spaces. In that case, we generalize monotonicity results by Miyamoto-Yagasaki and Benguria-Depassier-Loss to $p\ge2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_01992 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Monotonicity of the period and positive periodic solutions of a quasilinear equation Dolbeault, Jean García-Huidobro, Marta Manásevich, Raúl Analysis of PDEs Classical Analysis and ODEs 34C25, 35J92, 34L30, 34C23 We investigate the monotonicity of the minimal period of periodic solutions of quasilinear differential equations involving the $p$-Laplace operator. First, the monotonicity of the period is obtained as a function of a Hamiltonian energy in two cases. We extend to $p\ge2$ classical results due to Chow-Wang and Chicone for $p=2$. Then we consider a differential equation associated with a fundamental interpolation inequality in Sobolev spaces. In that case, we generalize monotonicity results by Miyamoto-Yagasaki and Benguria-Depassier-Loss to $p\ge2$. |
| title | Monotonicity of the period and positive periodic solutions of a quasilinear equation |
| topic | Analysis of PDEs Classical Analysis and ODEs 34C25, 35J92, 34L30, 34C23 |
| url | https://arxiv.org/abs/2301.01992 |