Fractional Lane-Emden Hamiltonian systems

Abstract

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

17 pages, 2 figures