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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A remark on the existence of positive periodic solutions of superlinear parabolic problems


Author: Maria J. Esteban
Journal: Proc. Amer. Math. Soc. 102 (1988), 131-136
MSC: Primary 35B10,; Secondary 35K60
MathSciNet review: 915730
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Abstract: We prove the existence of a solution for the following problem:

$\displaystyle {\partial _t}u - \Delta u = f(t,x,u){\text{ in (}}0,T) \times \Om... ...0){\text{ in }}\Omega ,\;\quad u = 0{\text{ on (}}0,T) \times \partial \Omega ,$

where $ \Omega $ is a bounded domain of $ {R^N}$ and the function $ f(t,x, \cdot )$ grows more slowly than $ {u^\alpha }$ at $ + \infty $, with $ \alpha {\text{ < }}N/(N - 2)$.

On démontre ici l'existence d'une solution positive pour le problème parabolique périodique suivant

\begin{displaymath}\begin{gathered}{\partial _t}u - \Delta u = f(t,x,u){\text{ i... ...u = 0{\text{ on (}}0,T) \times \partial \Omega ,\end{gathered} \end{displaymath}

$ \Omega $ est un domaine borné de $ {R^N}$ et la fonction $ f(t,x, \cdot )$ croit plus lentement que $ {u^\alpha }$ à l'infini, avec $ \alpha {\text{ < }}N/(N - 2)$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0915730-7
PII: S 0002-9939(1988)0915730-7
Keywords: Parabolic nonlinear problems, superlinearity, periodic solutions
Article copyright: © Copyright 1988 American Mathematical Society