Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain (Q1347794)

The paper is concerned with stable subharmonic solutions of the time-periodic spatially inhomogeneous reaction-diffusion equation \[ u_t=\Delta u+f(z, t, u)\qquad (x\in\Omega,\;t>0) \] where \(\Omega\) is a bounded domain in a Euclidean space and \(f\) is periodic in \(t\) with period \(\tau>0\). Besides, various boundary conditions are imposed. The authors show that stable subharmonic solutions exist on any spatial domain, provided the nonlinearity is chosen suitably. By definition, a solution \(u(x, t)\) is subharmonic if it is periodic in \(t\) with the minimal period \(k\tau\) with \(k>1\).