Periodic solutions of certain variational inequalities

Abstract

For a class of variational inequalities (quasilinear parabolic problems with a one-sided ‘obstacle’) arising from the Hamilton-Jacobi-Bellman formulation of certain periodic stochastic optimal control problems, it is shown that there are unique periodic solutions. AMS Subject Classification: 35B10, 49A29, 49C99.

Keywords:

• Variational inequality
• partial differential equations
• parabolic
• existence
• uniqueness
• maximum principle
• periodic
• nonlinear
• obstacle
• stochastic optimal control
• Hamilton-Jacobi-Bellman equation

AMS(MOS)::

• 35B10
• 49A29
• 49C99

^∗This research has been partially supported under grants AFOSR-82-0271 and AFOSR-87-0190

^∗This research has been partially supported under grants AFOSR-82-0271 and AFOSR-87-0190

Notes

^∗This research has been partially supported under grants AFOSR-82-0271 and AFOSR-87-0190