Asymptotic Behavior Of Solutions For Systems Of Periodic Reaction Diffusion Equations With Nonlocal Boundary Value Conditions

In this thesis we study the existence of periodic solutions and the asymptotic behavior of general time-dependent solutions for periodic reaction-diffusion equations with nonlocal boundary value conditions, the existence of periodic solutions or periodic quasisolutions and the asymptotic behavior of general time-dependent solutions for periodic reaction-diffusion systems with nonlocal boundary value conditions. The whole thesis is made up of three chapters.In Chapter 1, we establish the upper and lower solutions method of the existence of periodic solutions and the local asymptotic behavior for scalar periodic reaction-diffusion equations with nonlocal boundary value conditions.In Chapter 2, we apply the results of Chapter 1 to establish the upper and lower solutions method of the existence of periodic solutions or periodic quasisolutions and the local asymptotic behavior for periodic reaction-diffusion systems with nonlocal boundary value conditions. Three cases will be investigated: (1) Quasimonotone nondecreasing systems; (2) Mixed quasimonotone systems; (3) A nonquasimonotone 2-system. As an extension, we shall also consider similar problems for mixed quasimonotone reaction-diffusion systems with nonlocal boundary value conditions which kernel Ki(x,y) is alternating sign.Finally, in Chapter 3, we use the above results to investigate the existence of positive periodic solutions and asymptotic behavior of solutions for the logistic equation with nonlocal boundary value conditions.