Complex and real valued solutions for fractoinal Helmholtz equation

In this paper, we are concerned with the limiting absorption principle for the fractional Helmholtz equation, By establishing the boundedness estimate for the resolvent of fractional Helmholtz operator, we obtain the nontrivial Lq(Rn) complex valued solutions for (0.1). By setting up a dual variational framework, we also obtain the real valued solutions for (0.1) via a non-vanishing principle.