Multiple solutions for the fractional p-Laplacian with jumping reactions

2021/04/05 by Silvia Frassu, Frassu, Silvia, Antonio Iannizzotto +1
Computer Science · Mathematics · #35P30 #35R11 #47H11 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2104.01937

openalex publication_date 2021/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a nonlinear elliptic equation driven by the degenerate fractional p-Laplacian, with Dirichlet type condition and a jumping reaction, i.e., (p-1)-linear both at infinity and at zero but with different slopes crossing the principal eigenvalue. Under two different sets of hypotheses, entailing different types of asymmetry, we prove the existence of at least two nontrivial solutions. Our method is based on degree theory for monotone operators and nonlinear fractional spectral theory.

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