Xiaoyan Li, Bian-Xia Yang
This article concerns the existence and multiplicity of radially symmetric nodal solutions to the nonlinear equation
where are general Hamilton-Jacobi-Bellman operators, μ is a real parameter and 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 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.
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| Xiaoyan Li |
Department of Mathematics and Statistics
Northwest Normal University
Lanzhou, Gansu 730000, China
| Bian-Xia Yang |
College of Science
Northwest A&F University
Yangling, Shaanxi 712100, China
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