Anisotropic (p, q)-Equations with Asymmetric Reaction Term

We consider a Dirichlet problem driven by the anisotropic (p, q)-Laplacian (double phase problem) and with a reaction term which exhibits asymmetric behavior as \(x\rightarrow \pm \infty \) $x\to \pm \infty$ . Using variational tools, truncation, and comparison techniques and critical groups, we prove a multiplicity theorem producing four nontrivial solutions all with sign information and ordered.