Gelfand type quasilinear elliptic problems with quadratic gradient terms

In this paper, for 00λ⁎>0, and there exists a minimal regular positive solution for every λ∈(0,λ⁎)λ∈(0,λ⁎). We also prove, under suitable conditions depending on the dimension N and the parameters p  , m1m1, m2m2, that for λ=λ⁎λ=λ⁎ there exists a minimal regular positive solution. Moreover we characterize minimal solutions as those solutions satisfying a stability condition in the case m1=m2m1=m2.