We study positive C 1 ( Ω ¯ ) solutions to classes of boundary value problems of the form − Δ p u = g ( x , u , c ) in Ω , u = 0 on ∂ Ω , where Δ p denotes the p -Laplacian operator defined by Δ p z : = div ( | ∇ z | p − 2 ∇ z ) ; 1$"> p > 1 , 0$"> c > 0 is a parameter, Ω is a bounded domain in R N ; N ≥ 2 with ∂ Ω of class C 2 and connected (if N = 1 , we assume that Ω is a bounded open interval), and g ( x , 0 , c ) < 0 for some x ∈ Ω (semipositone problems). In particular, we first study the case when g ( x , u , c ) = λ f ( u ) − c where 0$"> λ > 0 is a parameter and f is a C 1 ( [ 0 , ∞ ) ) function such that f ( 0 ) = 0 , 0$"> f ( u ) > 0 for 0 < u < r and f ( u ) ≤ 0 for u ≥ r . We establish positive constants c 0 ( Ω , r ) and λ * ( Ω , r , c ) such that the above equation has a positive solution when c ≤ c 0 and λ ≥ λ ∗ . Next we study the case when g ( x , u , c ) = a ( x ) u p − 1 − u γ − 1 − c h ( x ) (logistic equation with constant yield harvesting) where p$"> γ > p and a is a C 1 ( Ω ¯ ) function that is allowed to be negative near the boundary of Ω . Here h is a C 1 ( Ω ¯ ) function satisfying h ( x ) ≥ 0 for x ∈ Ω , h ( x ) ≢ 0 , and max x ∈ Ω ¯ h ( x ) = 1 . We establish a positive constant c 1 ( Ω , a ) such that the above equation has a positive solution when c < c 1 Our proofs are based on subsuper solution techniques.