ABSTRACT
This chapter focuses on the time-periodic parabolic boundary value problems. The upper and lower solutions method for time-periodic parabolic boundary value problems, and the principal eigenvalue of periodic parabolic eigenvalue problems form the bulk of the chapter. For time-periodic parabolic boundary value problems, there is also the maximum principle which takes the following version. However, existence and uniqueness of solutions are not completely clear for time-periodic parabolic boundary value problem of linear equations. For time-periodic parabolic boundary value problems, some good properties of initial-boundary value problems may not hold, and however, some properties of elliptic boundary value problems are inherited. It uses the principle eigenvalue and the upper and lower solutions method of time-periodic parabolic boundary value problem, together with the comparison principle of initial-boundary value problem to study the time-periodic problem of logistic equation.
