Existence and nonexistence of positive solutions for nonlocal problems with inhomogeneous strong Allee effect

In this paper, we deal with the nonlocal elliptic problem with inhomogeneous strong Allee effect-M∫Ω1p∣∇u∣pdxΔpu=λf(x,u),inΩ,u=0,on∂Ω,where the nonlocal coefficient M∫Ω1p∣∇u∣pdx is a continuous function of ∫Ω12∣∇u∣2dx. By means of variational approach, we prove that the problem has at least two positive solutions for large λ under suitable hypotheses about nonlinearity. We also prove some nonexistence results.