Three nontrivial solutions of a nonlocal problem involving critical exponent

2018/12/04 by Soni, Amita, Choudhuri, D.
#35J20 #35J35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.01327

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 amp; = |u|^p_s^∗-2u+λf(x,u) in Ω,
u amp; = 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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