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Infinitely many solutions of a second-order \(p\)-Laplacian problem with impulsive condition. (English) Zbl 1224.34091
Summary: Using critical point theory and the method of lower and upper solutions, we present a new approach to obtain the existence of solutions to a \(p\)-Laplacian impulsive problem. As applications, we get unbounded sequences of solutions and sequences of arbitrarily small positive solutions of the \(p\)-Laplacian impulsive problem.

MSC:
34B37 Boundary value problems with impulses for ordinary differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
34A45 Theoretical approximation of solutions to ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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