Exponential growth in age-structured two-sex populations Maia Martcheva * Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395, USA Received 31 December 1997; accepted 9 October 1998 Abstract We consider a continuous age-structured two-sex population model which is given by a semilinear system of partial dierential equations with nonlocal boundary conditions and is a simpler case of Fredrickson±Hoppensteadt model. The non-linearity is intro- duced by a source term, called from its physical meaning, the marriage function. The explicit form of the marriage function is not known; however, there is an understanding among the demographers about the properties it should satisfy. We have shown that the homogeneity property of the non-linearity leads to the fact that the system supports exponentially growing persistent solutions using a general form of the marriage function and its properties. This suggests that the model can be viewed as a possible extension of the one-sex stable population theory to monogamously mating two-sex popula- tions. Ó 1999 Elsevier Science Inc. All rights reserved. Keywords: Two-sex populations; Pair formation; Age-structure; Persistent solutions 1. Introduction A stable population is a population which is closed to migration and the age-speci®c birth and death rates are time invariant. Such a population is modeled by McKendrick±von Foerster model [18,2]. * Present address: Department of Applied Mathematics, Polytechnic University, Six Metrotech Center, Brooklyn, NY 11201, USA. Fax: +1-718 260 3139; e-mail: mayam@magnus.poly.edu 0025-5564/99/$ ± see front matter Ó 1999 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 5 - 5 5 6 4 ( 9 8 ) 1 0 0 7 4 - 3 Mathematical Biosciences 157 (1999) 1±22