A liouville theorem for indefinite fractional diffusion equations and its application to existence of solutions

Abstract

In this work we obtain a Liouville theorem for positive, bounded solutions of the equation where (-δ)s stands for the fractional Laplacian with s 2 (0; 1), and the functions h and f are nondecreasing. The main feature is that the function h changes sign in R, therefore the problem is sometimes termed as indefinite. As an application we obtain a priori bounds for positive solutions of some boundary value problems, which give existence of such solutions by means of bifurcation methods.