Abstract
In this paper, by topological methods, we investigate the global structures of positive solution set of the following semipositone problem: { − ( p ( x ) u ′ ( x ) ) ′ + q ( x ) u ( x ) = λ f ( x , u ( x ) ) , 0 ≤ x ≤ 1 , α 0 u ( 0 ) + β 0 u ′ ( 0 ) = 0 , α 1 u ( 1 ) + β 1 u ′ ( 1 ) = 0 . We also obtain the existence of multiple positive solutions of the above problem. The nonlinear term f ( x , u ) may be nonsingular and singular at x = 0 or x = 1 , also may be negative for some values x and u , and λ is a parameter.
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