Abstract

In this paper, we investigate the following third-order three-point semipositone boundary value problems: ( ) ( , ) 0, (0,1); (0) ( ) (1) 0, u t f t u t u u u             Under the conditions that the nonlinear term ( , ) f t u :(0,1) (0, ) ( , )   is continuous, i.e., we allow that the nonlinear term f is both semipositone and lower unbounded. By using the fixed-point index theory, the existence of positive solution and many positive solutions are obtained. Key words : Third-order three-point semipositone boundary value problems, lower unbounded, positive solutions,fixed-point index theory. 2000 MR. Subiect Classification 34B 16.