Nodal solutions for a nonlinear fourth-order eigenvalue problem

Ma, Ru Yun and Thompson, Bevan (2008) Nodal solutions for a nonlinear fourth-order eigenvalue problem. Acta Mathematica Sinica, English Series, 24 1: 27-34. doi:10.1007/s10114-007-1009-6


Author Ma, Ru Yun
Thompson, Bevan
Title Nodal solutions for a nonlinear fourth-order eigenvalue problem
Journal name Acta Mathematica Sinica, English Series   Check publisher's open access policy
ISSN 1439-8516
1439-7617
0583-1431
Publication date 2008-01-01
Year available 2008
Sub-type Article (original research)
DOI 10.1007/s10114-007-1009-6
Open Access Status DOI
Volume 24
Issue 1
Start page 27
End page 34
Total pages 8
Editor B. Li
F. Lin
K. Chang
Place of publication Heidelberg, Germany
Publisher Springer-Verlag
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
0101 Pure Mathematics
Abstract We are concerned with determining the values of A, for which there exist nodal solutions of the fourth-order boundary value problem
Formatted abstract
We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem

           y´´´´ = λɑ(x)f(y),          0 < x < 1,
           y(0) = y(1) = y´´(0) = y´´(1) = 0,

where λ is a positive parameter, ɑC([0, 1], (0, ∞)), fC (ℝ, ℝ) satisfies f(u)u > 0 for all u ≠ 0. We give conditions on the ratio f(s)/s, at infinity and zero, that guarantee the existence of nodal solutions. The proof of our main results is based upon bifurcation techniques.
© The Editorial Office of AMS & Springer-Verlag 2008

Keyword Multiplicity results
Eigenvalues
Bifurcation methods
Nodal zeros
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

 
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Created: Thu, 19 Feb 2009, 23:27:59 EST by Marie Grove on behalf of School of Mathematics & Physics