A global bifurcation theorem for a multiparameter positone problem and its application to the one-dimensional perturbed Gelfand problem

Huang, Shao-Yuan and Hung, Kuo-Chih and Wang, Shin-Hwa: A global bifurcation theorem for a multiparameter positone problem and its application to the one-dimensional perturbed Gelfand problem. Electronic journal of qualitative theory of differential equations 99. pp. 1-25. (2019)

[img] Cikk, tanulmány, mű
ejqtde_2019_099.pdf

Download (4MB)

Abstract

We study the global bifurcation and exact multiplicity of positive solutions for u 00(x) + λ fε(u) = 0, − 1 < x < 1, u(−1) = u(1) = 0, where λ > 0 is a bifurcation parameter, ε ∈ Θ is an evolution parameter, and Θ ≡ (σ1, σ2) is an open interval with 0 ≤ σ1 < σ2 ≤ ∞. Under some suitable hypotheses on fε , we prove that there exists ε0 ∈ Θ such that, on the (λ, kuk∞)-plane, the bifurcation curve is S-shaped for σ1 < ε < ε0 and is monotone increasing for ε0 ≤ ε < σ2. We give an application to prove global bifurcation of bifurcation curves for the one-dimensional perturbed Gelfand problem.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 99
Page Range: pp. 1-25
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.99
Uncontrolled Keywords: Gelfand probléma, Bifurkáció
Additional Information: Bibliogr.: p. 24-25. ; összefoglalás angol nyelven
Date Deposited: 2020. Jan. 28. 09:35
Last Modified: 2020. Jan. 28. 09:35
URI: http://acta.bibl.u-szeged.hu/id/eprint/66366

Actions (login required)

View Item View Item