Existence Of Solutions For The Skyrme Model And Nonlinear Optical Vortices

In this thesis, we investigate the Skyrme model arising from the gauge field and the optical vortices model from the nonlinear optical theory. For the Skyrme model, we establish the existence theorem of the two-point boundary value problem by the direct variational method. The related properties of the solutions are also studied. For the optical vortices model, we first obtain the existence theorem of solutions for optical vor-tices by the constrainted variational approach and the lower bound estimates of the wave propagation constant β are also derived; secondly, we use the mountain pass lemma to prove the existence of the saddle point solutions.