Homoclinic solutions for fractional Hamiltonian systems via variational method
We study the multiplicity of weak nonzero solutions for fractional Hamiltonian systems of the form $$_{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha} u(t)) +L(t)u(t)=a(t)\nabla V(t,u(t)),\quad t\in \mathbb{R},$$ where $\alpha\in (1/2,1]$, $_{-\infty}D_{t}^{\alpha}$ and $_{t}D_{\infty}^{\alpha}$ are...
| Autores: | , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Santiago de Compostela (USC) |
| Repositorio: | Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela |
| Idioma: | inglés |
| OAI Identifier: | oai:minerva.usc.gal:10347/45450 |
| Acceso en línea: | https://hdl.handle.net/10347/45450 |
| Access Level: | acceso abierto |
| Palabra clave: | Variational methods Homoclinic solutions 1202 Análisis y análisis funcional |
| Sumario: | We study the multiplicity of weak nonzero solutions for fractional Hamiltonian systems of the form $$_{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha} u(t)) +L(t)u(t)=a(t)\nabla V(t,u(t)),\quad t\in \mathbb{R},$$ where $\alpha\in (1/2,1]$, $_{-\infty}D_{t}^{\alpha}$ and $_{t}D_{\infty}^{\alpha}$ are left and the right Liouville-Weyl fractional derivatives of order $\alpha$ on real line $\mathbb{R}$, $L(t)$ is a positive defined symmetric $n\times n$ matrix and $V:\mathbb{R}\times \mathbb{R}^n\to \mathbb{R}$ satisfies specific growth conditions. A result is proved using variational method and the generalized Clark's theorem. Some recent results are extended and improved. |
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