Multiplicity of solutions for a class of fractional elliptic problem\n with critical exponential growth and nonlocal Neumann condition

2019/10/06 by Claudianor O. Alves, Alves, Claudianor O., César E. Torres Ledesma +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1910.02422

openalex publication_date 2019/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the existence and multiplicity of weak solutions\nfor the following class of fractional elliptic problem\n\
label00
left

beginaligned (-
Delta)^
frac12u + u\namp;= Q(x)f(u)
;
;
mboxin
;
;
R
setminus (a,b)


mathcalN_1/2u(x) amp;=\n0
;
;
mboxin
;
;(a,b),
endaligned
right. where a,b\∈ R\nwith a<b, (-\Δ)^\(1)/(2) denotes the fractional Laplacian operator\nand \N_s is the nonlocal operator that describes the Neumann\nboundary condition, which is given by
mathcalN_1/2u(x) =
frac1
pi\n
int
_{R
setminus (a,b)}
fracu(x) - u(y)|x-y|²dy,
;
;x
in [a,b].\n

Citations

• Singularly perturbed Neumann problem for fractional Schrödinger equations

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