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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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