LIOUVILLE THEOREM FOR INDEFINITE FRACTIONAL PARABOLIC EQUATION INVOLVING PSEUDO-RELATIVISTIC SCHRÖDINGER OPERATORS

In this paper, we study the following indefinite fractional parabolic equation involving pseudo-relativistic Schrödinger operators <p class="disp_formula">$\begin{equation*}\frac{\partial u}{\partial t}(x, t)+(-\Delta+m^2)^su(x, t)=a(x_1)f(u(x, t)), \ \ \mbox{in}\ { \mathbb R^N}\times\mathbb R, \end{equation*}$ where <inline-formula><tex-math id="M1">$0&lt;s&lt;1$</tex-math></inline-formula> and the mass <inline-formula><tex-math id="M2">$m&gt;0$</tex-math></inline-formula>. We first prove the monotonicity of positive bounded solutions by using the method of moving planes. Moreover, the nonexistence of positive bounded solutions is established.