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 beenaccomplished in the literature for nonlocal initial problems with nonlinear boundary conditions. It isthe purpose of this paper to prove the existence results for solutions to a semilinear parabolic PDEwith 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 spacesand generalized Poincare operators play an important role in proving the existence of solutions.