Robin double-phase problems with singular and superlinear terms

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 lambda f (z, x), which is Caratheodory and (p - 1)-superlinear at x is an element of R, without satisfying the Ambrosetti-Rabinowitz condi-tion. 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 lambda > 0 varies. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This study explores a nonlinear Robin problem driven by the sum of p-Laplacian and q-Laplacian, considering competing effects of a singular term and a parametric perturbation. Using variational tools and comparison techniques, the study proves a bifurcation-type result describing changes in the set of positive solutions as the parameter lambda > 0 varies.