Steady States Of A Predator-prey System With Holling Type Ⅴ Functional Response

This thesis is devoted to the study of a predator-prey systemwith Holling functional response. First, we discuss the stability of the positive constant solutions of the system by using the basic spectrum theory of operators. Then we give an a priori estimate (positive upper and lower bounds) for positive steady solutions by applying the Maximum Principle and the Harnack inequality, based on which we derive some existence and nonexistence results for nonconstant steady solutions by using appropriate energy integrals and the topological degree theory. Finally, we discuss the bifurcation phenomena of the positive constant steady state solutions by taking the diffusion coefficients as bifurcation parame-ters.