# Global Bifurcation from Zero in Some Fourth-Order Nonlinear Eigenvalue Problems

Global Bifurcation from Zero in Some Fourth-Order Nonlinear Eigenvalue Problems In this paper, we study the nonlinear eigenvalue problem for ordinary differential equations of fourth order with a spectral parameter in the boundary condition. Global bifurcation of nontrivial solutions of this problem is investigated. We prove the existence of two families of unbounded continua of the set of solutions to this problem bifurcating from points and intervals of the line of trivial solutions. Moreover, it is shown that these continua are contained in classes of functions possessing oscillating properties of the eigenfunctions of the corresponding linear problem and their derivatives. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Malaysian Mathematical Sciences Society Springer Journals

# Global Bifurcation from Zero in Some Fourth-Order Nonlinear Eigenvalue Problems

, Volume 44 (2) – Aug 11, 2020
12 pages

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# References (21)

Publisher
Springer Journals
Copyright © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2020
ISSN
0126-6705
eISSN
2180-4206
DOI
10.1007/s40840-020-00989-6
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we study the nonlinear eigenvalue problem for ordinary differential equations of fourth order with a spectral parameter in the boundary condition. Global bifurcation of nontrivial solutions of this problem is investigated. We prove the existence of two families of unbounded continua of the set of solutions to this problem bifurcating from points and intervals of the line of trivial solutions. Moreover, it is shown that these continua are contained in classes of functions possessing oscillating properties of the eigenfunctions of the corresponding linear problem and their derivatives.

### Journal

Bulletin of the Malaysian Mathematical Sciences SocietySpringer Journals

Published: Aug 11, 2020