Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain

Peter Poláčik; Eiji Yanagida

doi:10.3934/dcds.2002.8.209

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2002, Volume 8, Issue 1: 209-218. Doi: 10.3934/dcds.2002.8.209

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Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain

Peter Poláčik^1, and
Eiji Yanagida^2,

1.
Institute of Applied Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava
2.
Mathematical Institute Tohoku University, 6-3Aoba, Aramaki, Aoba-ku, Sendai-shi, 980-8578

Received: January 2001

Revised: July 2001

Published: January 2002

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Abstract

The paper is concerned with stable subharmonic solutions of timeperiodic spatially inhomogeneous reaction-diffusion equations. We show that such solutions exist on any spatial domain, provided the nonlinearity is chosen suitably. This contrasts with our previous results on spatially homogeneous equations that admit stable subharmonic solutions on some, but not on arbitrary domains.

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Mathematics Subject Classification: 35K57, 35B10, 35B40.

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