Abstract
In this paper, we prove that if is a radially symmetric, signchanging stationary solution of the nonlinear heat equation (NLH) ut u =juj u; in the unit ball of R N , N = 3, with Dirichlet boundary conditions, then the solution of (NLH) with initial value blows up in nite time if j 1j > 0 is suciently small and if > 0 is suciently small. The proof depends on showing that the inner product of with the rst eigenfunction of the linearized operator L = ( + 1)j j is nonzero.
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