Krasnoselskii's fixed-point theorem in a cone is used to discuss the existence of positive solutions to semipositone right focal eigenvalue problems ( − 1 ) n − p u ( n ) ( t ) = λ f ( t , u ( t ) , u' ( t ) , … , u ( p − 1 ) ( t ) ) , u ( i ) ( 0 ) = 0 , 0 ≤ i ≤ p − 1 , u ( i ) ( 1 ) = 0 , p ≤ i ≤ n − 1 , where n ≥ 2 , 1 ≤ p ≤ n − 1 is fixed, f : [ 0 , 1 ] × [ 0 , ∞ ) p → ( − ∞ , ∞ ) is continuous with f ( t , u 1 , u 2 , … , u p ) ≥ − M for some positive constant M .