Johnny Henderson, Nickolai Kosmatov
In this article we study a well-known boundary value problem
With in place of , many authors studied the existence of positive solutions of both the positone problems with and the semi-positone problems for . It is well-known that the standard method successfully applied to the semi-positone problem with does not work for in the same setting. We treat the latter as a problem with a sign-changing term rather than a semi-positone problem. We apply Krasnosel'skii's fixed point theorem  to obtain positive solutions.
Submitted June 10, 2014. Published August 14, 2014.
Math Subject Classifications: 34B15, 34B16, 34B18.
Key Words: Green's function; fixed point theorem; positive solutions; third-order boundary-value problem.
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| Johnny Henderson |
Department of Mathematics
Waco, TX 76798-7328, USA
| Nickolai Kosmatov |
Department of Mathematics and Statistics
University of Arkansas at Little Rock
Little Rock, AR 72204-1099, USA
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