Complex and Real Valued Solutions for Fractional Helmholtz Equation

ABSTRACT In this paper, we are concerned with the limiting absorption principle for the fractional Helmholtz equation: , where and are two real parameters. By establishing the boundedness estimate for the resolvent of fractional Helmholtz operator, we obtain the nontrivial complex valued solutions for the fractional Helmholtz equation. By setting up a dual variational framework, we also obtain the real valued solutions for the fractional Helmholtz equation via a non‐vanishing principle.