title: A nonlinear l(2)-stability analysis for two-species population dynamics with dispersal.
abstract: The nonlinear L(2)-stability (instability) of the equilibrium states of two-species population dynamics with dispersal is studied. The obtained results are based on (i) the rigorous reduction of the L(2)-nonlinear stability to the stability of the zero solution of a linear binary system of ODEs and (ii) the introduction of a particular Liapunov functional V such that the sign ofdV/dt along the solutions is linked directly to the eigenvalues of the linear problem.
authors.affiliation: University of Naples Federico II, Department of Mathematics and Applications "R. Caccioppoli", Complesso Universitario Monte S. Angelo. Via Cinzia, 80126 Napoli, Italy. rionero@unina.it.
authors.forename: Salvatore
authors.initials: S
authors.lastname: Rionero