Infinitely many sign changing solutions of an elliptic problem involving\n critical Sobolev and Hardy-Sobolev exponent

2014/10/29 by Mousomi Bhakta, Bhakta, Mousomi
Computer Science · Mathematics · #35B33 #35J60 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1410.7880

openalex publication_date 2014/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the existence and multiplicity of sign changing solutions of the\nfollowing equation begincases -\Δ u = \μ\n|u|^2^\⋆-2u+ frac|u|^2^*(t)-2u|x|^t+a(x)u ∈ \n\Ω, u=0 \on \∂\Ω, endcases where \Ω is a\nbounded domain in R^N, 0\∈\∂\Ω, all the principal curvatures of\n\∂\Ω at 0 are negative and \μ\≥ 0, a>0, N\≥ 7, \n0<t<2, 2^\⋆=\(2N)/(N-2) and 2^\⋆(t)=\(2(N-t))/(N-2).\n

Citations

• Sign changing solution of the hardy-sobolev-maz'ya equation

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