Article ID Journal Published Year Pages File Type
841465 Nonlinear Analysis: Theory, Methods & Applications 2011 9 Pages PDF
Abstract

We prove the nonexistence of solutions for a prescribed mean curvature equation {−div(∇u1+|∇u|2)=λ|u|p−1u,x∈BR⊆Rn,u=0,x∈∂BR, when p⩾1p⩾1 and the positive parameter λλ is small. The result extends theorems of Narukawa and Suzuki, and Finn, from the case of n=2,p=1n=2,p=1 to all n⩾2,p⩾1n⩾2,p⩾1. Moreover, our proof is very simple and the result is not limited to positive (and negative) solutions. We also show that a similar result for positive solutions is still true if |u|p−1u|u|p−1u is replaced by the exponential nonlinearity eu−1eu−1.

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