Advances in Differential Equations

Positivity, change of sign and buckling eigenvalues in a one-dimensional fourth order model problem

Hans-Christoph Grunau

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Abstract

We study a one dimensional Dirichlet problem of fourth order and a corresponding "buckling eigenvalue problem" under Dirichlet boundary conditions. These problems may serve as model problems for "Orr-Sommerfeld" like boundary and eigenvalue problems. It turns out that eigenvalue curves in appropriate parameter domains look completely different than for the same equation under so called Navier boundary conditions. Further emphasis is laid on positivity properties, and also here, fundamental differences with Navier conditions arise: It may e.g. happen that one has infinitely many linearly independent positive eigenfunctions. Connections and analogies with the clamped plate boundary value problem on families of deformed domains are discussed.

Article information

Source
Adv. Differential Equations Volume 7, Number 2 (2002), 177-196.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651850

Mathematical Reviews number (MathSciNet)
MR1869560

Zentralblatt MATH identifier
1031.34085

Subjects
Primary: 34B15: Nonlinear boundary value problems
Secondary: 35J40: Boundary value problems for higher-order elliptic equations 74G60: Bifurcation and buckling

Citation

Grunau, Hans-Christoph. Positivity, change of sign and buckling eigenvalues in a one-dimensional fourth order model problem. Adv. Differential Equations 7 (2002), no. 2, 177--196. https://projecteuclid.org/euclid.ade/1356651850.


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