#### Document Type

Article

#### Publication Date

1-1-1986

#### Publication Title

SIAM Journal on Mathematical Analysis

#### Abstract

We study the existence, uniqueness and stability properties of solutions to the integral equation q,=Q[q] with q,(-)=l, q,()=0. Here Q[u](x)=f K(x-y)g(y,u(y))dy is defined on functions bounded between 0 and 1, K is a probability density function and g(x,u)=[s(x)u +u]/[l+s(x)u2+ o(x)(1-u)2] according to a population genetics model. The hypotheses on g are based on the biological assumption that the homozygotes, that is individuals with genotypes AA or aa, are best fit to survive near opposite ends of the one-dimensional habitat.

#### Suggested Citation

Lui, Roger
(1986). A Nonlinear Integral Operator Arising from a Model in Population-Genetics .4. Clines. *SIAM Journal on Mathematical Analysis, 17*(1), 152-168.

Retrieved from:
http://digitalcommons.wpi.edu/mathematicalsciences-pubs/26

#### Volume

17

#### Issue

1

#### First Page Number

152

#### Last Page Number

168

#### DOI

10.1137/0517015

#### Publisher Statement

© 1986, SIAM Publications.