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A multiplicity result including a sign-changing solution for an inhomogeneous Neumann problem with critical exponent

Published online by Cambridge University Press:  26 March 2007

Norimichi Hirano
Affiliation:
Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan (hirano@math.sci.ynu.ac.jp; shioji@math.sci.ynu.ac.jp)
Naoki Shioji
Affiliation:
Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan (hirano@math.sci.ynu.ac.jp; shioji@math.sci.ynu.ac.jp)

Abstract

We study the existence of multiple solutions for the problem

and we show that at least one of them is sign changing. Here Ω is a bounded domain in ℝN with N ⩾ 5 whose boundary is of class C2, /ν is the outward normal derivative, and fLN/2(Ω) whose L2N/(N+2)(Ω) norm is sufficiently small.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2007

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