Nonzero nonnegative solutions of population models of Ricker types and theory of limit inferiors and superiors

Abstract

The existence of nonzero nonnegative solutions of the population models of Ricker types governed by systems of second-order elliptic boundary value problems is studied. New theory on limit inferiors and superiors of functions at points and ∞ in product Banach spaces is established. New results on the limit inferiors, limit superiors and limits for monotone and mixed monotone functions at points in ordered Banach spaces and at ∞ in the Euclidean spaces are obtained. These results on limit inferiors and superiors are used to obtain the existence of nonzero nonnegative solutions of the population models of Ricker types.

Existence and uniqueness of solutions of nonlinear Cauchy‐type problems for first‐order fractional differential equations

“…The population models of Ricker type governed by system of second-order uniformly elliptic differential equations and system of second-order ordinary differential equations were studied in [21,22] and [23], respectively. These models are motivated by the population models with the growth rates of Ricker type governed by difference equations and first-order ordinary differential equations in [24][25][26][27][28][29] and [30,31], respectively.…”