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On a class of p ‐fractional Laplacian equations with potential depending on parameter
Author(s) -
Massar Mohammed,
Talbi Mohamed
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.6078
Subject(s) - mathematics , class (philosophy) , operator (biology) , fractional laplacian , laplace operator , nonlinear system , mountain pass theorem , p laplacian , mathematical analysis , mountain pass , pure mathematics , mathematical physics , physics , boundary value problem , biochemistry , chemistry , repressor , quantum mechanics , artificial intelligence , computer science , transcription factor , gene
We discuss the existence of solutions for a class of nonlinear equations driven by the fractional p ‐Laplacian operator of the form( − Δ ) p s u + λ s V ( x , λ ) | u | p − 2 u = f ( x , u ) inR N , where 0< s <1< p < ∞ , N > p s and λ is a positive parameter. By combining variational techniques with a version of the mountain pass theorem without Palais‐Small (PS) condition, we establish the existence of nontrivial solutions for the above equation under certain appropriate assumptions on nonlinearity and weight functions.