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The paper establishes a link between the stability of the semigroup e(−Γ+M)t and the spectral radius of Γ−1M in ordered Banach spaces. On the one hand our result allows utilizing simple estimates for the eigenvalues of −Γ+M in order to provide general conditions for the convergence of the successive approximation scheme for semilinear operator equations. On the other hand, this paper helps examining...
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