Multiplicity results for fractional magnetic problems involving\n exponential growth

2019/06/27 by Pawan Kumar Mishra, João Marcos do Ó, Mishra, Pawan Kumar +4
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1906.12013

openalex publication_date 2019/06/27 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We study the following fractional elliptic equations of the type,\n\(-
Delta)
^frac12_A u =
lambda u+f(|u|)u ,
;
textrmin \n
;(-1, 1),
; u=0
;
textrmin
;
mathbb R
setminus (-1, 1), nwhere \λ is a positive real parameter and (-\Δ) ^frac12_A is the\nfractional magnetic operator with A: mathbb R\→ mathbb R being a smooth\nmagnetic field. Using a classical critical point theorems, we prove the\nexistence of multiple solutions in the non-resonant case when the nonlinear\nterm f(t) has a critical exponential growth in the sense of Trudinger-Moser\ninequality.\n

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