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International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 1, Pages 41-46

Super and subsolutions for elliptic equations on all of n

Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran

Received 26 October 2001

Copyright © 2002 Hindawi Publishing Corporation. 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.


By construction sub and supersolutions for the following semilinear elliptic equation u(x)=λg(x)f(u(x)), xn 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:n such that g is smooth and is negative at infinity.