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 $\lambda f(z,x)$, which is Carathéodory and $(p-1)$-superlinear at $x\in \mathbb{R},$ 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 $\lambda >0$ varies.

References in corpus (6)

• Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves
• Double-phase problems and a discontinuity property of the spectrum
• Double-phase problems with reaction of arbitrary growth
• Existence and multiplicity of solutions for double-phase Robin problems
• Positive solutions for nonlinear nonhomogeneous parametric Robin problems
• Pairs of positive solutions for resonant singular equations with the $p$-Laplacian