Qualitative Analysis On A Class Of Reaction Diffusion Equations

With the serious problem of ecological protection, the importance of basic subjects in the field of biology application also gradually highlights. Important branch of partial differential equations as applied mathematics in the biological field applications, mainly rely on the establishment of ecological model, based on the reaction diffusion equation (group) qualitative analysis to determine the rule of population dynamic development, plays a positive role in promoting the ecological development.The main topic is to consider the boundary value problem of a predator prey model with the modified Holling type-Ⅱ functional response, focus on the existence of positive solutions, multiplicity and stability.The first chapter analyzes the application background and significance of applied mathematical in the field of biology, prey on the origin and development of the model and Holling response function, and the research progress of elliptic equations with homogeneous Dirichlet boundary. The second chapter use priori estimate and topological degree in cones to calculate fixed point indices. Third, four chapters use the conclusions which the second chapter gains to study effects of parameters on the existence of positive solutions, stability and multiplicity of coexistence states. The final chapter lists a specific model, verifies its function to satisfy conditions which the general function have, draw the conclusions.