Existence and multiplicity for radially symmetric solutions to Hamilton-Jacobi-Bellman equations

This article concerns the existence and multiplicity of radially symmetricnodal solutions to nonlinear equation $$\displaylines{ -\mathcal{M}_\mathcal{C}^{\pm}(D^2u)=\mu f(u) \quad \text{in } \mathcal{B},\cru=0 \text{on \partial\mathcal{B}, }$$ where \(\mathcal{M}_\mathcal{C}^{\pm}\) are general Hamilton-Jacobi-Bellman operators, (\mu\) is a real parameter \(\mathcal{B}\) unit ball. By using bifurcation theory, we determine range \(\mu\) in which above problem has one or multiple nodal according behavior \(f\) at 0 infinity, whether satisfies signum condition \(f(s)s>0 \) for \(s\neq 0\) not. For more information see https://ejde.math.txstate.edu/Volumes/2021/31/abstr.html