Fractional Lane-Emden Hamiltonian systems

Abstract

In this work, our interest lies in proving the existence of solutionsto the following Fractional Lane-Emden Hamiltonian system:(−∆)su = Hv(x, u, v) in Ω,(−∆)sv = Hu(x, u, v) in Ω,u = v = 0 in Rn \ Ω.The method, that can be traced back to the work of De Figueiredo and Felmer[6], is flexible enough to deal with more general nonlocal operators and makeuse of a combination of fractional order Sobolev spaces together with functionalcalculus for self-adjoint operators.