Multiple solutions for perturbed quasilinear elliptic problems - Bartolo, Rossella; Candela, Anna Maria; Salvatore, Addolorata (Topological Methods in Nonlinear Analysis, 2023)
We investigate the existence of multiple solutions for the (p,q)-quasilinear elliptic problem \[ cases -Δ_p u -Δ_q u = g(x, u) + ε h(x,u) & in Ω, u=0 & on Ω, cases \] where 1< p< q< +∞, Ω is an open bounded domain of R^N, the nonlinearity g(x,u) behaves at infinity as |u|^q-1, εR and hC(Ω×R,R). In spite of the possible lack of a variational structure of this problem, from suitable assumptions on g(x,u) and appropriate procedures and estimates, the existence of multiple solutions can be proved for small perturbations.