Positive Solutions And Optimal Control Of A Juvenile-adult Model

In this thesis, by using the method of lower and upper solutions and bifurcation theory, we study the existence of positive solutions of a juvenile-adult model. Ap-plying a cost-benefit functional, we study the optimal control of this juvenile-adult model. The main results are described as follows.1.In the first two chapters, we use the method of lower and upper solutions and bifurcation theory to study the juvenile-adult model And we obtain the sufficient condition for the existence of positive solutions and non-existence of positive solutions. The main results extend and improve the cor-responding ones of Brown and Zhang [J. Math. Anal. Appl.,2003]. The main results also extend and improve the corresponding ones of Bouguima [Nonlinear Anal. RWA.,2008], Henaoui [Nonlinear Anal. RWA.,2012] and Ruyun Ma [Appl. Math. Comp.,2014].2.In the third chapter, we consider the juvenile-adult model And we study the the uniqueness of positive solution and the optimal control prob-lem. The main results extend and improve the corresponding ones of Arino [Proc. Edinburgh Math. Soci.,2000] and Canada [J. Math. Anal. Appl.,2001]. More-over. we study the optimal control problem.