Asymptotic Regimes of an Integro-Difference Equation with Discontinuous Kernel

This paper is concerned with an integral equation that models discrete time dynamics of a population in patchy landscape. The patches the domain are reflected through discontinuity kernel operator at finite number points whole domain. We prove existence and uniqueness stationary state under certain assumptions on principal eigenvalue linearized growth term as well. also derive criteria which undergoes extinction (in case solution 0 everywhere).