Multiple solutions for superlinear fractional p-Laplacian equations

Abstract We study a Dirichlet problem driven by the (degenerate or singular) fractional p -Laplacian and involving a $$(p-1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -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.