Reversed S-Shaped Bifurcation Curve for a Neumann Problem

Autor: Hui Xing, Hongbin Chen, Ruofei Yao
Jazyk: angličtina
Rok vydání: 2018
Předmět:
Zdroj: Discrete Dynamics in Nature and Society, Vol 2018 (2018)
Druh dokumentu: article
ISSN: 1026-0226
1607-887X
DOI: 10.1155/2018/5376075
Popis: We study the bifurcation and the exact multiplicity of solutions for a class of Neumann boundary value problem with indefinite weight. We prove that all the solutions obtained form a smooth reversed S-shaped curve by topological degree theory, Crandall-Rabinowitz bifurcation theorem, and the uniform antimaximum principle in terms of eigenvalues. Moreover, we obtain that the equation has exactly either one, two, or three solutions depending on the real parameter. The stability is obtained by the eigenvalue comparison principle.
Databáze: Directory of Open Access Journals
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