Periodicity and boundedness of solutions of generalized differential equations of growth

Sufficient conditions are given for the existence of periodic solutions of differential equations, having as special cases the equations used to describe the competition between two species. The Poincaré bifurcation theory is used to secure one set of conditions, and another set of conditions is secured through a generalization of a method of V. Volterra. The question of boundedness is considered and conditions implying boundedness and conditions implying that populations are bounded away from zero are given. Several integrable classes of systems are discovered and a particular example having periodic solutions is examined in detail. This research was supported by the Air Force Office of Scientific Research under Grant 62-207.