Pairs of positive solutions for singular pp-Laplacian equations with a pp-superlinear potential

We consider a singular parametric elliptic equation driven by the pp-Laplacian and with a pp-superlinear potential which does not satisfy the Ambrosetti–Rabinowitz condition. Using variational arguments, combined with truncation techniques and the method of upper and lower solutions, we show that there exists a λ∗>0λ∗>0 such that if the parameter λλ is in (0,λ∗)(0,λ∗), then the problem has two ordered smooth positive strong solutions.