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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  and
Naoki Shioji
Norimichi Hirano
Affiliation:
Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan ([email protected]; [email protected])
Naoki Shioji
Affiliation:
Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan ([email protected]; [email protected])
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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 f ∈ LN/2(Ω) whose L2N/(N+2)(Ω) norm is sufficiently small.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 2 , 2007 , pp. 333 - 347
Copyright
Copyright © Royal Society of Edinburgh 2007

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