Self-similar solutions of focusing semi-linear wave equations in R^N

In this paper, we prove the existence of a countable family of regular spherically symmetric self-similar solutions to focusing energy-supercritical semi-linear wave equations ∂ttu-Δu=|u|p-1uinRN,where N≥ 3 , 1+4N-2<p and, if N≥ 4 , p≤1+4N-3. This was previously known only in the case N= 3 , for integer p (see Bizoń et al. in Nonlinearity 20(9):2061–2074, 2007). We also study the asymptotics of these solutions.