The Study Of Two Variational Problem

In this paper, we mainly study two models which are the mathematical problem of the DNA dynamic model and the Baby-Skyrm model on the sphere. In the first model, we only consider a pair of base case while ignoring the interaction between base pairs because of the complexity of the problem, we establish the existence of the periodic solution by constrained minimizing method. In the second model, the existence of the energy-minimizing solutions for the model on the sphere is proved by variational method. Some properties of the solutions are also established.