Multiple Solutions to (p,q)-Laplacian Problems with Resonant Concave Nonlinearity

Abstract

Abstract The existence of multiple solutions to a Dirichlet problem involving the ( p , q ) ${(p,q)}$ -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 - Δ p ${-\Delta_{p}}$ in W 0 1 , p ⁢ ( Ω ) ${W^{1,p}_{0}(\Omega)}$ and exhibits a concave behavior near zero.