Tuesday, September 15, 2026 — 12:05 pm — laboratorio M0.1, edificio Matematica
Critical $(p,q)$-Laplacian problems with near-critical perturbations
Abstract: We study quasilinear elliptic problems driven by the $(p,q)$-Laplace operator in which the nonlinearities combine the critical Sobolev term with a superlinear subcritical perturbation of near-critical growth. By exploiting the strength of this perturbation, we establish the existence of nontrivial solutions even in low-dimensional regimes that are not accessible by previous approaches. The analysis is variational and relies on a general linking construction based on a nonlinear eigenvalue sequence defined via the Fadell–Rabinowitz cohomological index, together with refined energy estimates that accommodate both resonant and nonresonant situations. We also address nonhomogeneous versions of the problem, proving the existence of multiple nontrivial solutions when the forcing term is sufficiently small.