A bifurcation theorem for the p-logistic equation

We consider a p-logistic equation with an equidiffusive reaction. Using variational methods and truncation techniques, we show that there is a critical parameter value λ∗ > 0 such that for λ > λ∗ the problem has a unique positive smooth solution, and for λ ∈ (0, λ∗] the problem has no positive solution.