Solutions of Partial Differential Equations Arising from Stochastic Optimal Control Problems and Applications
吳彥霖先生國立中央大學數學系 下午 1:30–2:20 鴻經館 107室Abstract:
In this talk, we are concerned with studying some second order elliptic partial differential equations. We are devote to establishing some qualitative properties of solutions, including existence, uniqueness and structure of solutions to three specific types of nonlinear elliptic equations.
First, we study a gradient constraint equation which is related to a stochastic optimal control problem. We offer the existence and uniqueness of positive radial solutions with certain behavior under weaker conditions on nonlinearity. Second, we consider a semilinear elliptic equation on the hyperbolic space. The asymptotic behavior, existence and uniqueness of positive singular solutions at the origin are proved. In addition, we discuss the structure of solutions of various types via the Pohozaev identity. Finally, we deal with the Hardy-Sobolev equations and investigate behaviors, existence and uniqueness of solutions for different exponents.