Extinction in two species nonautonomous nonlinear competitive system

A two species nonautonomous nonlinear competitive system is studied in this paper. It is shown that if the coefficients are continuous, bounded above and below by positive constants and satisfy certain inequalities, then one of the components will be driven to extinction while the other one will stabilize at the certain positive solution of a nonlinear single species model. Our result not only generalizing but also improving the result of Li and Chen (2006).