On spectra of a certain class of quadratic operator pencils with one-dimensional linear part

  • V. N. Pivovarchik

Abstract

We consider a class of quadratic operator pencils that occur in many problems of physics. The part of such a pencil linear with respect to the spectral parameter describes viscous friction in problems of small vibrations of strings and beams. Patterns in the location of eigenvalues of such pencils are established. If viscous friction (damping) is pointwise, then the operator in the linear part of the pencil is one-dimensional. For this case, rules in the location of purely imaginary eigenvalues are found.
Published
25.05.2007
How to Cite
PivovarchikV. N. “On Spectra of a Certain Class of Quadratic Operator Pencils With One-Dimensional Linear Part”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 5, May 2007, pp. 702–716, http://umj.imath.kiev.ua/index.php/umj/article/view/3339.
Section
Research articles