Multiplicity and stability result for semilinear parabolic equations

Pages: 271 - 280, Volume 2, Issue 2, April 1996

doi:10.3934/dcds.1996.2.271       Abstract        Full Text (1420.7K)       Related Articles

Norimichi Hirano - Department of Mathematics, Yokohama National University, 156 Tokiwadai Hodogaya-ku - Yokohama, Japan (email)
Wen Se Kim - Department of Mathematics, Dong-A University, Handan-2Dong, Saha-ku, Pusan, South Korea (email)

Abstract: 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 $h \in C([0,2\pi],C^1_0(\overline{\Omega})).$

Keywords:  Multiplicity and stability, semilinear parabolic equations.
Mathematics Subject Classification:  35Kxx.

Received: November 1995;      Published: February 1996.