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Some results on principal eigenvalues for periodic parabolic problems with weight

Published online by Cambridge University Press:  17 April 2009

U. Kaufmann
Affiliation:
FaMAF, Universidad Nacional de Córdoba, Ciudad Universitaria, (5000) Córdoba, Argentina, e-mail: kaufmann@mate.uncor.edu
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Abstract

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Let Ω ⊂ ℝN be a bounded domain. We study existence and uniqueness of principal eigenvalues for the Dirichlet periodic parabolic problem with weight Lu = λmu in Ω × ℝ when the independent coefficient of the differential operator L is not necessarily positive.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Beltramo, A., Über den Hauptteigenwert von peridish-parabolischen Differiantialoperatoren, Ph.D. Thesis (Univ. of Zurich, Zurich, 1984).Google Scholar
[2]Beltramo, A. and Hess, P., ‘On the principal eigenvalues of a periodic-parabolic operator’, Comm. Partial Differential Equations 9 (1984), 919941.CrossRefGoogle Scholar
[3]Daners, D., ‘Periodic-parabolic eigenvalues problems with indefinite weight functions’, Arch. Math. 68 (1997), 388397.CrossRefGoogle Scholar
[4]Daners, D., ‘Existence and perturbation of principal eigenvalues for a periodic-parabolic problem’, Electron. J. Differ. Equ. Conf. 5 (2000), 5167.Google Scholar
[5]Daners, D. and Koch-Medina, P., Abstract evolution equations, periodic problems and applications, Pitman Research Notes in Mathematics 279 (Longman Scientific and J. Wiley & Sons, Harlow and New York, 1992).Google Scholar
[6]Fleckinger, J., Hernández, J. and de Thélin, F., ‘Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems’, (Preprint).Google Scholar
[7]Godoy, T., Guerin, A. and Paczka, S., ‘On positive solutions of some periodic parabolic eigenvalue problem with a weight function’, Rend. Sem. Mat. Univ. Padova 101 (1999), 117.Google Scholar
[8]Godoy, T. and Kaufmann, U., ‘On principal eigenvalues for periodic parabolic problems with optimal condition on the weight function’, J. Math. Anal. Appl. 262 (2001), 208220.CrossRefGoogle Scholar
[9]Godoy, T., Dozo, E. Lami and Paczka, S., ‘The periodic parabolic eigenvalue problem with L weight’, Math. Scand. 81 (1997), 2034.CrossRefGoogle Scholar
[10]Hess, P., Periodic-parabolic boundary value problems and positivity, Pitmans Research in Mathematics 247 1992 (Longman Scientific and J. Wiley & Sons, Harlow and New York).Google Scholar
[11]Hess, P., On positive solutions of semilinear periodic-parabolic problems, Lecture Notes in Math. 1076 (Springer-Verlag, Berlin, Heidelberg, New York), pp. 101114.Google Scholar