On a class of singular anisotropic $(p,q)$-equations

TL;DR

This paper studies a class of anisotropic $(p,q)$-Laplacian equations with singular and superlinear terms, analyzing how the solutions change as a parameter varies using variational and bifurcation methods.

Contribution

It introduces a bifurcation analysis for anisotropic $(p,q)$-Laplacian problems with singular and superlinear reactions, employing variational, truncation, and comparison techniques.

Findings

Existence of positive solutions depending on parameter values

Bifurcation phenomena characterized as parameter varies

Use of variational and comparison methods for analysis

Abstract

We consider a Dirichlet problem driven by the anisotropic $(p,q)$-Laplacian and with a reaction that has the competing effects of a singular term and of a parametric superlinear perturbation. Based on variational tools along with truncation and comparison techniques, we prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter varies.