Monotonicity of solutions for fractional equations with De Giorgi type nonlinearities
Monotonicity of solutions for fractional equations with De Giorgi type nonlinearities
In this paper, we develop a sliding method for the fractional Laplacian. We first obtain the key ingredients needed in the sliding method either in a bounded domain or in the whole space, such as narrow region principles and maximum principles in unbounded domains. Then using semi-linear equations involving the …