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INHOMOGENEOUS PERIODIC PARABOLIC PROBLEMS WITH INDEFINITE DATA

Part of: Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  06 September 2011

T. GODOY  and
U. KAUFMANN
T. GODOY
Affiliation:
FaMAF, Universidad Nacional de Córdoba, (5000) Córdoba, Argentina (email: godoy@mate.uncor.edu)
U. KAUFMANN*
Affiliation:
FaMAF, Universidad Nacional de Córdoba, (5000) Córdoba, Argentina (email: kaufmann@mate.uncor.edu)
*
✉For correspondence; e-mail: kaufmann@mate.uncor.edu
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Abstract

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Let Ω⊂ℝN be a smooth bounded domain and let f⁄≡0 be a possibly discontinuous and unbounded function. We give a necessary and sufficient condition on f for the existence of positive solutions for all λ>0 of Dirichlet periodic parabolic problems of the form Lu=h(x,t,u)+λf(x,t), where h is a nonnegative Carathéodory function that is sublinear at infinity. When this condition is not fulfilled, under some additional assumptions on h we characterize the set of λs for which the aforementioned problem possesses some positive solution. All results remain true for the corresponding elliptic problems.

Keywords

periodic parabolic problemsindefinitesub- and supersolutionselliptic problems

MSC classification

Secondary: 35K20: Initial-boundary value problems for second-order parabolic equations 35B10: Periodic solutions

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 516 - 524
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The research was partially supported by Secyt-UNC and ANPCYT.

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