Article,
An application of Wazewski's method to a non-linear boundary value problem which arises in population genetics
Journal of Mathematical Biology, 2 (3): 241-249 (1975)
DOI: 10.1007/BF00277153
Abstract
A non-linear boundary value problem is treated using the principle of T. Wazewski. The equation is
where s(x) is non zero near +co. The boundary condition on p at
+ co is 0 and I according as sen s ( + co) is - 1 or + 1. Two essentially different eases are treated,
namely sgn s ( + ~ ) = + s e n s ( - co). A radially symmetric problem with x ~ R 2 is also discussed.
d2/dxZp(x)+s(x) p ( l - p ) = 0
The Wazewski principle allows one to describe the sets of initial data which satisfy the boundary
conditions at + co and at - co and to show how they intersect.
The problem arises in the study of clines in population genetics theory.
