  The main subject of this paper is a computer assisted stability proof for a
stationary solution of reaction diffusion equations in one dimensional space.
We use Nakao's numerical verification method to enclose a stationary solution
of reaction-diffusion equations. Considering the linearized stability of the
solution, a method of excluding eigenvalues in a half plane is adopted. We
first focus on the eigenvalues for an operator linearized at an approximate
solution. An excluding theorem is presented such that we know under some
condition, and there is no eigenvalue in some disks. Some computable criteria
are constructed to apply the theorem in a computer. And also the invertibility
of some operator is proved theoretically in the paper. However, we need the
information of the eigenvalues for the operator linearized at the exact
solution. This can be obtained by combining with the verification results of
the solution. Then we judge the stability of the solution from the domain where
the eigenvalues are located. At last there are some verification results.
