Multiple solutions for superlinear fractional $p$-Laplacian equations

Antonio Iannizzotto, Vasile Staicu, Vincenzo Vespri

Published 2024-11-15Version 1

We study a Dirichlet problem driven by the (degenerate or singular) fractional $p$-Laplacian and involving a $(p-1)$-superlinear reaction at infinity, not necessarily satisfying the Ambrosetti-Rabinowitz condition. Using critical point theory, truncation, and Morse theory, we prove the existence of at least three nontrivial solutions to the problem.