Remark on an infinite semipositone problem with indefinite weight and falling zeros

In this work, we consider the positive solutions to the singular problem where 0 0 are constants, Ω is a bounded domain with smooth boundary , Δ is a Laplacian operator, and is a continuous function. The weight functions m ( x ) satisfies m ( x ) ∈ C (Ω) and m ( x ) > m 0 > 0 for x ∈ Ω and also || m || ∞ = l 0, M > 0, p > 1 such that alu − M ≤ f ( u ) ≤ Au p for all u ∈ [0, ∞ ). We prove the existence of a positive solution via the method of sub-supersolutions when and c is small. Here λ 1 is the first eigenvalue of operator − Δ with Dirichlet boundary conditions.