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

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January 2002, 8(1): 209-218. doi: 10.3934/dcds.2002.8.209

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

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

Received January 2001 Revised July 2001 Published October 2001

Abstract
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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.

Keywords: monotonicity method., Stable subharmonic solutions, periodic parabolic equations.

Mathematics Subject Classification: 35K57, 35B10, 35B4.

Citation: Peter Poláčik, Eiji Yanagida. Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 209-218. doi: 10.3934/dcds.2002.8.209

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