On Comparison Principles for Parabolic Equations with Nonlocal Boundary Conditions

The positivity of solutions for parabolic problems is the base of comparison principle which is important in monotonic methods used for these problems. Recently, Yin [1] developed several results in applications of the comparison principle, especially on nonlocal problems. Earlier works on problems with nonlocal boundary conditions can be found in [2], and some of references can be found in [1, 3]. In the literature, for example [2, 4–6], a restriction on the boundary condition (see (2.1)) of the kind ∫