Linear And Nonlinear Selections Of Spreading Speed For Nonlocal Dispersal Monostable Equations

In this paper,we consider that the question of spreading speed for nonlocal dispersal equations with monostable nonlinearity.we consider that the sufficient condition for the nonlinear and linear selections of the spreading speed established by comparison principle and upper and lower solutions which is based on abstract method when the nonlinear term is nondegenerate at zero point,we give a further depiction of rationality which minimal speed is defined by linear speed when nonlocal dispersal equations with Fisher-kpp nonlinearity,meanwhile,in this situation,we give the mechanism of speed selection which the equation has discrete delay.when we consider that nonlinear term is degenerate,because of the linear speed is zero,and critical speed is nonnegative,hence the critical speed can not be determined by the linear speed,however we can give a depiction of critical speed through special long-time behavior of traveling wave solution,at the same time,we get the nonlinear selection conditions,and we specifically describe spreading speed for nonlocal dispersal equation with degenerate nonlinearity through ,which is sufficiently small,thus we give a certain characterization in different angles.