Necessary and sufficient condition for existence and uniqueness of nodal solutions to sublinear elliptic equations

Abstract

This paper deals with a sublinear elliptic equation $\Delta u + f(u)=0$ in a ball with the Dirichlet condition $u=0$ on the boundary. Under a suitable assumption on $f(\cdot)$, we establish the necessary and sufficient condition for the existence and uniqueness of radially symmetric nodal solutions.