Liouville-type theorem for logarithmic Laplacian systems in coercive epigraphs

This paper is concerned with the Dirichlet problem of logarithmic Laplacian equations and systems on unbounded regions. We first establish new narrow region principles for the logarithmic Laplacian equation and system in coercive epigraphs separately. Then by using the direct method of moving planes, we obtain a monotonicity result for the solutions of logarithmic Laplacian equations and a Liouville-type theorem for solutions of logarithmic Laplacian systems in coercive epigraphs.