Periodic solutions of fractional Laplace equations: Least period, axial symmetry and limit
We are concerned with periodic solutions of the fractional Laplace equation equation* (-_xx)^su(x)+F’(u(x))=0 in R, equation* where 0< s< 1. The smooth function F is a double-well potential with wells at +1 and -1. We show that the value of least positive period is 2π×(1/-F’’(0))^1/(2s)