Electronic Journal of Differential Equations,
Conference 05 (2000), pp. 51-67.

Title: Existence and perturbation of principal eigenvalues for a periodic-parabolic problem.

Authors: Daniel Daners (Brigham Young Univ., Provo, Utah, USA)
 
Abstract: 
  We give a necessary and sufficient condition for the existence of a
  positive principal eigenvalue for a periodic-parabolic problem with
  indefinite weight function. The condition was originally established
  by Beltramo and Hess [\textit{\frenchspacing Comm. Part. Diff.
  Eq.}, \textbf{9} (1984), 919--941] in the framework of the
  Schauder theory of classical solutions. In the present paper, the
  problem is considered in the framework of variational evolution
  equations on arbitrary bounded domains, assuming that the
  coefficients of the operator and the weight function are only
  bounded and measurable. We also establish a general perturbation
  theorem for the principal eigenvalue, which in particular allows
  quite singular perturbations of the domain. Motivation for the
  problem comes from population dynamics taking into account seasonal
  effects.

Published October 24, 2000.
Math Subject Classifications: 35K20, 35P05, 35B20, 47N20.
Key Words: principal eigenvalues; periodic-parabolic problems;
  parabolic boundary-value problems; domain perturbation.