Key points are not available for this paper at this time.
In this paper, we consider fractional equations involving the logarithmic Laplacian with indefinite nonlinearities: Formula: see text where Formula: see text represents a Lipschitz coercive epigraph. Our investigation begins by establishing a boundary estimate for antisymmetric functions and demonstrating the monotonicity of bounded positive solutions in coercive epigraphs, via the direct method of moving planes. Subsequently, we present a Liouville-type theorem for this nonlocal problem.
Liu et al. (2024) studied this question.