# American Institute of Mathematical Sciences

April  1996, 2(2): 271-280. doi: 10.3934/dcds.1996.2.271

## Multiplicity and stability result for semilinear parabolic equations

 1 Department of Mathematics, Yokohama National University, 156 Tokiwadai Hodogaya-ku - Yokohama 2 Department of Mathematics, Dong-A University, Handan-2Dong, Saha-ku, Pusan, South Korea

Received  November 1995 Published  February 1996

In this paper, we show the existence of stable and unstable periodic solutions for a semilinear parabolic equation

$\qquad\qquad \frac{\partial u}{\partial t}-\Delta_x u -\lambda_1 u +g(u) =s \phi + h$ in $R\times \Omega$

$\qquad\qquad u(t,x) =0$ on $R\times \partial \Omega$

$\qquad\qquad u(0,x)=u(2\pi, x)$ on $\Omega$

where $g$ is a continuous function on $R$, $\phi$ denotes the positve normalized eigenfunction corresponding to the first eigenvalue $\lambda_1$ of problem (L), $s \in R$, and $h \in C([0,2\pi],C^1_0(\overline{\Omega})).$

Citation: Norimichi Hirano, Wen Se Kim. Multiplicity and stability result for semilinear parabolic equations. Discrete & Continuous Dynamical Systems, 1996, 2 (2) : 271-280. doi: 10.3934/dcds.1996.2.271
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