Theorems about the Existence of Solutions to Problems with Nonlocal Initial Value

Recently much work has been devoted to nonlocal problems. However, very little has been accomplished in the literature for nonlocal initial problems with nonlinear boundary conditions. It is the purpose of this paper to prove the existence results for solutions to a semilinear parabolic PDE with linear homogeneous boundary conditions, and to other ones with nonlinear boundary conditions, provided the ordered upper and lower solutions are given. Semigroup, fractional order function spaces and generalized Poincaré operators play an important role in proving the existence of solutions. Supportedpartly by Research Grant 19531060 of China NSF and Grant 97024811 of the Foundation of Doctoral Program