in "Proceedings of Nonlinear Differential Equations, a
conference celebrating the sixtieth birthday of Alan C. Lazer,"

University of Miami, January 1999 (S. Cantrell and C. Cosner, eds.)

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

Citations on Google Scholar

University of Miami, January 1999 (S. Cantrell and C. Cosner, eds.)

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

Citations on Google Scholar

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
[*Comm. Part. Diff. Eq.*, **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. Finally, we establish a general perturbation theorem
for the principal eigenvalues, which in particular allows quite
singular perturbations of the domain. Motivation for the problem
comes from population dynamics taking into account seasonal
effects.

**AMS Subject Classification (1991):**
Primary: 35K20,
Secondary: 35P05, 35B20, 47N20

You can go to the original article.