Inthispaper,asystemofreaction-diffusionequationsarisinginanutrient-phytoplanktonpopulationsisinvestigated.Theequationsmodelasituationinwhichphytoplanktonpopulationispidedintotwogroups,namelysusceptiblephytoplanktonandinfectedphytoplankton.Anumberofexistenceandnon-existenceresultsaboutthenon-constantsteadystatesofareactiondiffusionsystemaregiven.Ifthediffusioncoefficientoftheinfectedphytoplanktonistreatedasbifurcationparameter,non-constantpositivesteady-statesolutionsmaybifurcatefromtheconstantsteady-statesolutionundersomeconditions.
