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
G. A. Afrouzi
and H. Ghasemzadeh
Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran
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.