Existence of Solutions for Front-Type Forced Waves of Leslie-Gower Predator-Prey Model in Shifting Habitats

In this paper, the definitions of front type and a pair of generalized upper and lower solutions are firstly described. Then, Leslie-Gower predator-prey model and the properties of kernel and growth rate function are expressed. The suitable upper and lower solutions combined with the Schauder's fixed-point theorem, fatou's lemma is utilized to solve the existence of nonnegative solution. Additionally, under the appropriate parameter assumptions, the existence of front type forced wave is verified.