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This study concerns the existence of positive weak solutions to boundary value problems of the form { −∆pu = g(x, u), x ∈ Ω, u(x) = 0, x ∈ ∂Ω, where ∆p is the so-called p-Laplacian operator i.e. ∆pz = div (|∇z|p−2∇z), p > 1, Ω is a smooth bounded domain in R (N ≥ 2) with ∂Ω of class C, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of the positive weak solution to special types of g(x, u). 94 S.H. Rasouli, G.A. Afrouzi and J. Vahidi / TJMCS Vol .3 No.1 (2011) 94-101

On Positive Weak Solutions For Some Nonlinear Elliptic Boundary Value Problems Involving The P-laplacian