Note on homoclinic solutions to nonautonomous Hamiltonian systems with sign-changing nonlinear part
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910818841395200 |
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| author | Bernini, Federico Bieganowski, Bartosz Strzelecki, Daniel |
| author_facet | Bernini, Federico Bieganowski, Bartosz Strzelecki, Daniel |
| contents | In the paper, we utilize the recent variational, abstract theorem to show the existence of homoclinic solutions to the Hamiltonian system $$ \dot{z} = J D_z H(z, t), \quad t \in \mathbb{R}, $$ where the Hamiltonian $H : \mathbb{R}^{2N} \times \mathbb{R} \rightarrow \mathbb{R}$ is of the form $$ H(z, t) = \frac12 Az \cdot z + Γ(t) \left( F(z) - λG(z) \right) $$ for some symmetric matrix $A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20908 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Note on homoclinic solutions to nonautonomous Hamiltonian systems with sign-changing nonlinear part Bernini, Federico Bieganowski, Bartosz Strzelecki, Daniel Classical Analysis and ODEs Analysis of PDEs 37C29, 37J46, 35A15, 58E05 In the paper, we utilize the recent variational, abstract theorem to show the existence of homoclinic solutions to the Hamiltonian system $$ \dot{z} = J D_z H(z, t), \quad t \in \mathbb{R}, $$ where the Hamiltonian $H : \mathbb{R}^{2N} \times \mathbb{R} \rightarrow \mathbb{R}$ is of the form $$ H(z, t) = \frac12 Az \cdot z + Γ(t) \left( F(z) - λG(z) \right) $$ for some symmetric matrix $A$. |
| title | Note on homoclinic solutions to nonautonomous Hamiltonian systems with sign-changing nonlinear part |
| topic | Classical Analysis and ODEs Analysis of PDEs 37C29, 37J46, 35A15, 58E05 |
| url | https://arxiv.org/abs/2405.20908 |