Infinite Semipositone Problems with Indefinite Weight and Asymptotically Linear Growth Forcing-terms

In this work, we study the existence of positive solutions to the singular problem −∆pu = λm(x)f(u)− u−α in Ω, u = 0 on ∂Ω, where λ is positive parameter, Ω is a bounded domain with smooth boundary, 0 < α < 1, and f : [0,∞]→ R is a continuous function which is asymptotically p-linear at ∞. The weight function is continuous satisfies m(x) > m0 > 0, ‖m‖∞ <∞. We prove the existence of a positive solution for a certain range of λ using the method of sub-supersolutions.