SIAM Journal on Mathematical Analysis
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.
Lui, R. (1986). A Nonlinear Integral Operator Arising from a Model in Population-Genetics .4. Clines. SIAM Journal on Mathematical Analysis, 17(1), 152-168. http://dx.doi.org/10.1137/0517015
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© 1986, SIAM Publications.