TITLE

Multiple sign-changing solutions for a semilinear Neumann problem and the topology of the configuration space of the domain boundary

AUTHOR(S)
Shioji, Naoki
PUB. DATE
July 2010
SOURCE
Calculus of Variations & Partial Differential Equations;Jul2010, Vol. 38 Issue 3/4, p317
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We study the existence of multiple sign-changing solutions of the problem where d > 0 is small enough, Ω is a domain in $${\mathbb{R}^{N}}$$ ( N ≥ 2) whose boundary is nonempty, compact and smooth and $${f \in C(\mathbb{R},\mathbb{R})}$$ is a function satisfying a subcritical growth condition. We give lower estimates of the number of the sign-changing solutions by the category of a set related to the configuration space $${\{(x,y)\in\partial\Omega\times\partial\Omega:x \neq y\}}$$ of the boundary ∂Ω.
ACCESSION #
50354935

 

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