Qualitative Study For Several Kinds Of Impulsive Fractional Differential Equations Boundary Value Problems

In this paper,we qualitatively study several kinds of impulsive nonlinear frac-tional differential equations.According to the different characteristics of the non-linear term of the impulsive nonlinear fractional differential equations,we choose the workspace of studying these kinds of impulsive nonlinear fractional differential equations by critical point theorem in the variational method and construct the variational functionals corresponding to these kinds of impulsive nonlinear frac-tional differential equations.Then we apply the critical point theorem to study the qualitative problems of these equations such as the existence and multiplicity of solutions.Firstly,we introduce the research background,application and cur-rent situation of fractional differential equations,and the main research problems in this paper.Then,we research the existence of infinitely many solutions for im-pulsive nonlinear fractional differential equations with two parameters,existence of solutions for impulsive nonlinear fractional differential equations with parame-ters and existence of infinitely many solutions for high-order nonlinear fractional differential equations boundary value problems with Bonanno and Molica Bisci critical point theorem,Morse theory and local linking theorem.