International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 1, Pages 41-46
doi:10.1155/S0161171202110428
Super and subsolutions for elliptic equations on all of ℝn
Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran
Received 26 October 2001
Copyright © 2002 G. A. Afrouzi and H. Ghasemzadeh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
By construction sub and supersolutions for the following
semilinear elliptic equation −△u(x)=λg(x)f(u(x)), x∈ℝn which arises in population genetics, we
derive some results about the theory of existence of solutions as
well as asymptotic properties of the solutions for every n and for the function g:ℝn→ℝ such that g is smooth and is negative at infinity.