Existence of solutions for an age-structured insect population model with a larval stage

In this paper we particularly draw attention to the existence of solutions which describe the maturation rates of an age-structured insect population model. Such models commonly divide the population into immature and mature individuals. Immature individuals are defined as individuals of age less than some threshold age τ, while adults are individuals of age exceeding τ. The model is represented by the nonlinear neutral differential equation with variable coefficients. The conditions, which guarantee that the population size tends to a nonnegative constant or nonconstant function are also established.