Positive solutions for the periodic-parabolic problem with large diffusion

In this paper, we study the positive solutions of the periodic-parabolic logistic equation with indefinite weight function and nonhomogeneous diffusion coefficient. By employing sufficient conditions to guarantee negative principal eigenvalue, we obtain the existence, uniqueness, and stability of the positive periodic solutions. Moreover, we prove that the positive periodic solution tends to the unique positive solution of the corresponding non-autonomous logistic equation when the diffusion rate is large.