Solvability For Several Kinds Of Differential Equations Boundary Value Problems With Instantaneous And Non-instantaneous Impulses

In this paper,we choose the appropriate fractional derivative space and construct the variational functionals corresponding to the p-Laplace fractional differential equations boundary value problem with instantaneous and noninstantaneous impulses,second-order Hamiltonian system with instantaneous and non-instantaneous impulses on time scales and p-Laplace differential equation boundary value problem with instantaneous and non-instantaneous impulses on time scales.The existence and multiplicity of solutions for these three kinds of differential equations boundary value problems are transformed into the existence and multiplicity of critical points for their corresponding variational functionals.Then,we apply the critical point theorem,classical Lax-Milgram theorem and fountain theorem to obtain some sufficient conditions for the existence and multiplicity of solutions for the three kinds of differential equations boundary value problems.The results obtained in this paper not only generalize some related results on the solvability of integer order impulsive differential equations boundary value problems,but also extend the application range of critical point theory in fractional differential equations boundary value problems with instantaneous and non-instantaneous impulses.