Existence of positive solutions for a class of semipositone problems with Kirchhoff operator

In this work we show a result of existence of positive solution for the followingnonlocal problem of Kirchhoff type−M(ˆΩ|∇u|2dx)∆u=f(u)−ainΩ, u= 0on∂Ω,whereΩ⊂RNis a smooth bounded domain,M, fare continuous nonnegative functions anda >0.By using mainly variational methods, we prove the existenceof a solution forasmall enough, undertwo different sets of hypotheses, which generalize the classical superlinear and sublinear problems