期刊
JOURNAL OF FUNCTIONAL ANALYSIS
卷 256, 期 3, 页码 747-776出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2008.11.023
关键词
Global branch; Bifurcation; Nodal curve; Nodal domain
类别
资金
- JSPS Research Fellowships
Let D subset of R-2 be a disk, and let f is an element of C-3. We assurne that there is a is an element of R such that f(a) = 0 and f'(a) > 0. In this article, we are concerned with the Neumann problem Delta u + lambda f(u) = 0 in D, partial derivative(v)u= 0 on partial derivative D. We show the following: There are unbounded continuums consisting of non-radically symmetric solutions emanating front the second and third eigenvalues. It f(u) = -u + u vertical bar u vertical bar(p-1) (a = 1) or it f is of bistable type, then the unbounded branches emanating from non-principal eigenvalues are unbounded in tile positive direction of lambda. The branch emanating from the second eigenvalue is unique near the bifurcation point up to rotation. The main tool of this article is the zero level set (the nodal curve) u(0) and u(x). (C) 2008 Elsevier Inc. All rights reserved.
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