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Existence of weak solutions for impulsive \(p\)-Laplacian problem with superlinear impulses. (English) Zbl 1266.34025

The author proves the existence of one and then of many weak solutions under subtle conditions for impulsive \(p\)-Laplacian problem by the critical point theory. The novelty is that the impulsive conditions are superlinear impulses.

MSC:

34A37 Ordinary differential equations with impulses
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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