Fractional Lane-Emden Hamiltonian systems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912196568547328 |
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| author | Dussel, Ignacio Ceresa Bonder, Julián Fernández Saintier, Nicolas Salort, Ariel |
| author_facet | Dussel, Ignacio Ceresa Bonder, Julián Fernández Saintier, Nicolas Salort, Ariel |
| contents | In this work, our interest lies in proving the existence of solutions to the following Fractional Lane-Emden Hamiltonian system: $$ \begin{cases} (-Δ)^s u = H_v(x,u,v) & \text{in }Ω,\\ (-Δ)^s v = H_u(x,u,v) & \text{in }Ω,\\ u=v=0 & \text{in } \R^n\setminusΩ. \end{cases} $$ The method, that can be traced back to the work of De Figueiredo and Felmer \cite{DF-F}, is flexible enough to deal with more general nonlocal operators and make use of a combination of fractional order Sobolev spaces together with functional calculus for self-adjoint operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11523 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Lane-Emden Hamiltonian systems Dussel, Ignacio Ceresa Bonder, Julián Fernández Saintier, Nicolas Salort, Ariel Analysis of PDEs 35J50, 35J47, 35D30, 35R11 In this work, our interest lies in proving the existence of solutions to the following Fractional Lane-Emden Hamiltonian system: $$ \begin{cases} (-Δ)^s u = H_v(x,u,v) & \text{in }Ω,\\ (-Δ)^s v = H_u(x,u,v) & \text{in }Ω,\\ u=v=0 & \text{in } \R^n\setminusΩ. \end{cases} $$ The method, that can be traced back to the work of De Figueiredo and Felmer \cite{DF-F}, is flexible enough to deal with more general nonlocal operators and make use of a combination of fractional order Sobolev spaces together with functional calculus for self-adjoint operators. |
| title | Fractional Lane-Emden Hamiltonian systems |
| topic | Analysis of PDEs 35J50, 35J47, 35D30, 35R11 |
| url | https://arxiv.org/abs/2501.11523 |