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Signed and sign‐changing solutions for a Kirchhoff‐type problem involving the fractional p ‐Laplacian with critical Hardy nonlinearity
Author(s) -
Gabert Rodrigo F.,
Rodrigues Rodrigo S.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5979
Subject(s) - mathematics , sobolev space , fractional laplacian , p laplacian , mountain pass theorem , sign (mathematics) , nehari manifold , nonlinear system , type (biology) , mathematical analysis , fractional calculus , mountain pass , pure mathematics , physics , ecology , quantum mechanics , biology , boundary value problem
In this paper, we study the existence of three solutions for a Kirchhoff equation involving the nonlocal fractional p ‐Laplacian considering Sobolev and Hardy nonlinearities at subcritical and critical growths. The proof is based on mountain pass theorem and constrained minimization in Nehari sets.