Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 31, pp. 1-19.

Title: Existence and multiplicity for radially symmetric solutions to 
       Hamilton-Jacobi-Bellman equations
       
Authors: Xiaoyan Li (Northwest Normal Univ., Lanzhou, Gansu, China)
         Bian-Xia Yang (Northwest A&F Univ., Yangling, Shaanxi, China)

Abstract:
This article concerns the existence and multiplicity of radially symmetric
 nodal solutions to the  nonlinear equation
 $$\displaylines{
 -\mathcal{M}_\mathcal{C}^{\pm}(D^2u)=\mu f(u) \quad \text{in } \mathcal{B},\cr
 u=0 \quad  \text{on } \partial\mathcal{B},
 }$$
 where $\mathcal{M}_\mathcal{C}^{\pm}$ are general Hamilton-Jacobi-Bellman  operators,
 $\mu$ is a real parameter and $\mathcal{B}$ is the unit ball.
 By using bifurcation theory, we determine the range of parameter μ in which the
 above problem has one or multiple nodal solutions according to the behavior of f
 at 0 and infinity, and whether f satisfies the signum condition f(s)s>0 for
 $s\neq0$ or not.

Submitted November 29, 2020. Published April 24, 2021.
Math Subject Classifications: 35B32, 35B40, 35B45, 35J60, 34C23.
Key Words: Radially symmetric solution; extremal operators; bifurcation; nodal solution.