In this paper, the existence and multiplicity of solutions for a coupled system of differential equations with instantaneous and noninstantaneous impulses are studied. By the virtue of variational methods, some new existence theorems of solutions are obtained. In addition, two examples are given to demonstrate our main results.

In this paper, three-point boundary value problems for second-orderp-Laplacian differential equations with instantaneous and noninstantaneous impulses are studied. The existence of at least one classical solution and infinitely many classical solutions is obtained by using variational methods and critical point theory. In addition, some examples are given to illustrate our main results.

In this paper, we consider a class of $ p $-Laplacian Kirchhoff-type fractional differential equations with instantaneous and non-instantaneous impulses. The existence of at least two distinct weak solutions and infinitely many weak solutions is obtained based on variational methods.

In this paper, we consider the existence, multiplicity and nonexistence of solutions for a class of $ p $-Laplacian differential equations with non-instantaneous impulses. By using variational methods and critical point theory, we obtain that the impulsive problem has at least one nontrivial solution, at least two nontrivial solutions and no nontrivial solution.

In this study, we consider the multiplicity of solutions for a new class of $p$-Laplacian fractional differential equations involving $\psi$-Caputo fractional derivative with instantaneous and non-instantaneous impulses. Since the $p$-Laplacian operator, $\psi$-Caputo fractional derivative and impulsive effects exist at the same time, it is difficult to establish the variational structure of the considered problem. By virtue of critical point theorems and variational methods, we give some new criteria to guarantee that the problem has at least two weak solutions and infinitely many weak solutions. Some recent results are improved and extended.

In this study, we consider a Kirchhoff-type second-order impulsive differential system with the Dirichlet boundary condition and obtain the existence and multiplicity of solutions to the impulsive problem via variational methods.