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Multiplicity and Concentration of Solutions for a Fractional Magnetic Kirchhoff Equation with Competing Potentials.

Authors :
Deng, Shengbing
Luo, Wenshan
Source :
Annales Henri Poincaré. Jul2024, Vol. 25 Issue 7, p3499-3528. 30p.
Publication Year :
2024

Abstract

This paper is concerned with the following fractional electromagnetic Kirchhoff equation with competing potentials and critical nonlinearity a ε 2 s + b ε 4 s - 3 [ u ] A / ε 2 (- Δ) A / ε s u + V (x) u = f (| u | 2 ) u + K (x) | u | 2 s ∗ - 2 u in R 3 , where ε > 0 is a small parameter, A ∈ C 0 , α (R 3 , R 3) with exponent α ∈ (0 , 1 ] , (- Δ) A / ε s is the fractional magnetic operator with s ∈ (3 4 , 1) , 2 s ∗ = 6 3 - 2 s is the fractional critical exponent, and a , b > 0 are fixed constants. Assuming that V, K and f satisfy some suitable conditions, we establish the multiplicity and concentration of solutions by variational methods and Ljusternik–Schnirelmann theory. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
14240637
Volume :
25
Issue :
7
Database :
Academic Search Index
Journal :
Annales Henri Poincaré
Publication Type :
Academic Journal
Accession number :
177993189
Full Text :
https://doi.org/10.1007/s00023-023-01372-4