Multiple solutions for the fractional p-Laplacian with jumping reactions

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, ent...

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Bibliographic Details
Published in:Journal of fixed point theory and applications 2023-02, Vol.25 (1), Article 25
Main Authors: Frassu, Silvia, Iannizzotto, Antonio
Format: Article
Language:English
Subjects:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-022-01019-7