Existence of a solution for a system related to the singularity for the 3D Zakharov system

Abstract

We prove the existence of infinitely many radial solutions for a system of equations in $\mathbb R^3$. Numerically, that is supposed to give the profile of an asymptotic self-similar blow-up solution of the Zakharov system in dimension three. For this, we use several techniques of ordinary differential equations and especially a kind of shooting method. Moreover, we give some properties of solutions, monotonicity, estimates at infinity and integral relations.