Variational method to the second-order impulsive partial differential equations with inconstant coefficients (I)

In the paper, we consider the existence of the solution of the second-order impulsive differential equations with inconstant coefficients. We change the second-order impulsive partial differential equation into the equivalent equation by transformation. By using the critical point theory of variational method and Lax-Milgram theorem, we obtain new results for the existence of the solution of the impulsive partial differential equations.