Multiple solutions to (p,q)-laplacian problems with resonant concave nonlinearity

Abstract

The existence of multiple solutions to a Dirichlet problem involving the (p,q)-Laplacian is investigated via variational methods, truncation-comparison techniques, and Morse theory. The involved reaction term is resonant at infinity with respect to the first eigenvalue of -Δp in W01,p (Ω) and exhibits a concave behavior near zero.