LS-Morse Index Formula For Extremely Small And Extremely Large Saddle Points

As soon as a saddle point is found,people will pay attention to its Morse index.The instability is an important character to a saddle point.For nondegenerate saddle points,the Morse indices can be used to measure their instability and classify them.In this thesis,a formula on the Morse index of minimax type saddle point by a Ljusternik-Schnirelman minimax algorithm is established,i.e.,a formula on the Morse index of LS-minimax type saddle point,is established.For nondegenerate minimax type saddle points,the formula clearly answers the question what their Morse indices are.Also,a numerical example on the Henon equation is presented to illustrate the application of the formula for calculating the Morse index of numerical solution in the computation of multiple solutions of the semilinear elliptic equation.