SCALAR CURVATURE TYPE PROBLEM ON THE THREE DIMENSIONAL BOUNDED DOMAIN

doi:10.1016/S0252-9602(16)30122-9

Abstract

Abstract:

In this paper we prove an existence result for the nonlinear elliptic problem:-△u=Ku⁵, 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.

Key words: scalar-curvature, critical point, limiting Sobolev exponent, variational problems with lack of compactness, blow up analysis

Mohamed BEN AYED, Habib FOURTI. SCALAR CURVATURE TYPE PROBLEM ON THE THREE DIMENSIONAL BOUNDED DOMAIN[J].Acta mathematica scientia,Series B, 2017, 37(1): 139-173.

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