A multiplicity theorem for p-superlinear p-Laplacian equations using critical groups and morse theory

摘要

We study a nonlinear elliptic equation driven by the Dirichlet p-Laplacian and with a Carathéodory nonlinearity. We assume that the nonlinearity exhibits a p-superlinear growth near infinity but need not satisfy the Ambrosetti–Rabinowitz condition. Using truncation techniques, minimax methods and Morse theory, we show that the problem admits at least three nontrivial solutions, two of which have constant sign (one positive, the other negative).