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Existence and multiplicity of solutions for an impulsive boundary value problem with a parameter via critical point theory. (English) Zbl 1219.34039
Summary: An impulsive boundary value problem with a parameter is considered. By using critical point theory, some criteria are obtained to guarantee that the impulsive problem has at least one solution, two solutions and infinitely many solutions when the parameter lies in different intervals. The results obtained are also valid and new for a problem discussed in the literature.
MSC:
34B37Boundary value problems for ODE with impulses
34B08Parameter dependent boundary value problems for ODE
58E05Abstract critical point theory
47J30Variational methods (nonlinear operator equations)
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