Robin double-phase problems with singular and superlinear terms

Abstract We consider a nonlinear Robin problem driven by the sum of p -Laplacian and q -Laplacian (i.e. the ( p , q ) -equation). In the reaction there are competing effects of a singular term and a parametric perturbation λ f ( z , x ) , which is Caratheodory and ( p − 1 ) -superlinear at x ∈ R , without satisfying the Ambrosetti–Rabinowitz condition. Using variational tools, together with truncation and comparison techniques, we prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter λ > 0 varies.