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

• Main Authors: Božena Dorociaková, Iveta Ilavská, Rudolf Olach
• Format: Article
• Language: English
• Published: University of Szeged 2017-09-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: population models; age structure; neutral delay equation; existence; fixed point theorem
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=5156
• ISSN: 1417-3875; 1417-3875

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 $\tau$, while adults are individuals of age exceeding $\tau$. 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.