The index of the complex eigenvalues of a parity progressive population operator (Q1604259)

This paper deals with the spectral property of a parity progressive population operator. Indeed the authors show that in order to get the asymptotic expansion of the solution of the corresponding population equation and obtain more profound stability results for the population system, one should investigate the index of the complex eigenvalues of the corresponding population operator. Under certain conditions, they prove that all the complex eigenvalues of the parity progressive population operator, except at most finitely many, are of index 1.