Some Research On Sturm-Liouville Boundary Value Problem And Logistic Population Model

Sturm-Liouville boundary value problems play an important role in the research and application of physics and engineering.It has been used to study some aspects of gas dynamics,fluid mechanics,nuclear physics,chemically reacting systems,the sources diffusion theory,and so on.In this paper,firstly,we prove a maximum principle on the Sturm-Liouville boundary value problems.And we combine the principle and fixed point theorem in Banach spaces to obtain a new result of positive solutions for the Sturm-Liouville problems.In our research,the restrictions on the nonlinear term f are weaker than usual that,and we extend the scope of the existence of positive solutions for the Sturm-Liouville boundary value problems,thus expand its application range.Finally,we transform the Logistic population model into a special form of the Sturm-Liouville boundary value problems.By utilizing the results of the Sturm-Liouville boundary value problems,we determine a critical patch size l~* involved in one-dimentional habitat that if l~*?l~*,the species survive under suitable ranges of the harvesting rate functions,if l?l~*,they would extinct.