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arXiv · 2501.11523

Fractional Lane-Emden Hamiltonian systems

Ignacio Ceresa Dussel·Julián Fernández Bonder·Nicolas Saintier·Ariel Salort
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Abstract

In this work, our interest lies in proving the existence of solutions to the following Fractional Lane-Emden Hamiltonian system: $$ \begin{cases} (-\Delta)^s u = H_v(x,u,v) & \text{in }\Omega,\\ (-\Delta)^s v = H_u(x,u,v) & \text{in }\Omega,\\ u=v=0 & \text{in } \R^n\setminus\Omega. \end{cases} $$ 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.

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Ignacio Ceresa Dussel, Julián Fernández Bonder, Nicolas Saintier, Ariel Salort. 2025-01-20. Fractional Lane-Emden Hamiltonian systems. https://arxiv.org/abs/2501.11523

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