This paper is devoted to the investigation of the existence of positive solutions to the second-order system with a -Laplacian and impulses
by using variational methods, where , , , , , and denote, respectively, the right and left limits of at , , , , , and .
The solutions of the problem are transferred, by considering an auxiliary problem, into the critical points of some functional, and the mountain pass theorem [see D. Guo, Nonlinear functional analysis, Shandong Science and Technology Press, Jinan (1985)] allows to prove the existence of at least one positive solution. Some results of [J. Simon, Lect. Notes Math. 665, 205–227 (1978; Zbl 0402.35017)], are also useful for the procedure. A particular case of this system has been studied in [X. Lin and D. Jiang, J. Math. Anal. Appl. 321, 501–514 (2006; Zbl 1103.34015)] by using the fixed point index in cones.