Entire solutions of the differential equation Δ;u = f(u)
Wolfgang L. Walter · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1981
Abstract The existence of spherically symmetric solutions of the equation ▵u = f(u) is proved for a large class of functions f(z). Among others, functions satisfying an inequality zf(z) A, and in particular the function f(z) = -sinh z, belong to this class.