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Scalar curvature type problem on the three dimensional bounded domain
Journal article   Peer reviewed

Scalar curvature type problem on the three dimensional bounded domain

Mohamed BEN AYED and Habib Fourti
Acta mathematica scientia, Vol.37(1), pp.139-173
01/2017
DOI: https://doi.org/10.1016/S0252-9602(16)30122-9

Abstract

35J20 35J60 blow up analysis critical point limiting Sobolev exponent scalar-curvature variational problems with lack of compactness
In this paper we prove an existence result for the nonlinear elliptic problem: Δu = K u5, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain of ℝ3 and K is a positive function in Ω¯. Our method relies on studying its corresponding subcritical approximation problem and then using a topological argument.

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