Existence of multiple solutions of p-fractional Laplace operator with sign-changing weight function

2014/08/20 by Goyal, Sarika, Sreenadh, K.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1408.4571

Abstract

In this article, we study the following p-fractional Laplacian equation (P_\la) \ - 2∫_{\mb Rⁿ}\frac|u(y)-u(x)|^p-2(u(y)-u(x))|x-y|^n+p\al dy = \la |u(x)|^p-2u(x) + b(x)|u(x)|^\ba-2u(x) in \Om u = 0 in \mb Rⁿ ∖\Om, u∈ W^\al,p(\mb Rⁿ). . where \Om is a bounded domain in \mb Rⁿ with smooth boundary, n> p\al, p≥ 2, \al∈(0,1), \la>0 and b:\Om⊂\mb Rⁿ \ra \mb R is a sign-changing continuous function. We show the existence and multiplicity of non-negative solutions of (P_\la) with respect to the parameter \la, which changes according to whether 1

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