Three nontrivial solutions of a nonlocal problem involving critical exponent

2018/12/04 by Amita Soni, Debajyoti Choudhuri, Soni, Amita +2
Computer Science · Mathematics · #35J20 #35J35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Combinatorics #Critical exponent #Degenerate energy levels #Differential Equations and Boundary Problems #Differential operator #Exponent #FOS: Mathematics #Fractional Laplacian #Geometry #Laplace operator #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Partial Differential Equations #Operator (biology) #Order (exchange) #Physics #Pure mathematics #Quantum mechanics #Scaling #Sobolev space #math.AP #msc:35J20 #msc:35J35 #p-Laplacian

paper · pdf · doi:10.48550/arxiv.1812.01327

published in arXiv (Cornell University) (Cornell University)

arxiv created 2018/12/04 · openalex publication_date 2018/12/04 · arxiv updated 2018/12/05 · openalex created_date 2018/12/11 · openalex updated_date 2026/07/28

Abstract

In this paper we will prove the existence of three nontrivial weak solutions of the following problem involving a nonlinear integro-differential operator and a term with critical exponent. \beginsplit -\mathscrL_Φu = |u|^p_s^∗-2u+λf(x,u) in Ω,
u = 0 in ℝ^N∖ Ω, \endsplit Here q∈(p, p_s^*), where p_s^* is the fractional Sobolev conjugate of p and -\mathscrL_Φ represents a general nonlocal integro-differential operator of order s∈(0,1). This operator is possibly degenerate and covers the case of fractional p-Laplacian operator.

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