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.
Multiple solutions for superlinear fractional p-Laplacian equations
Iannizzotto, Antonio
;Staicu, Vasile;Vespri, Vincenzo
2025-01-01
Abstract
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.
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