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

Abstract

This article concerns the existence and multiplicity of radially symmetric nodal solutions to the nonlinear equation -M±C (D2u) = μƒ(u) in B, u = 0 on ∂B, M±C are general Hamilton-Jacobi-Bellman operators, μ is a real parameter and 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 ƒ at 0 and ∞, and whether ƒ satisfies the signum condition ƒ(s)s > 0 for s ≠ 0 or not.