Electron. J. Differential Equations, Vol. 2021 (2021), No. 31, pp. 1-19.

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

Xiaoyan Li, Bian-Xia Yang

Abstract:
This article concerns the existence and multiplicity of radially symmetric nodal solutions to the nonlinear equation

where $\mathcal{M}_\mathcal{C}^{\pm}$ are general Hamilton-Jacobi-Bellman operators, μ 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.
DOI: https://doi.org/10.58997/ejde.2021.31

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Xiaoyan Li
Department of Mathematics and Statistics
Northwest Normal University
Lanzhou, Gansu 730000, China
email: 17242502@qq.com
Bian-Xia Yang
College of Science
Northwest A&F University
Yangling, Shaanxi 712100, China
email: yanglina7765309@163.com

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