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Zbl 1219.34039
Bai, Liang; Dai, Binxiang
Existence and multiplicity of solutions for an impulsive boundary value problem with a parameter via critical point theory. (English)
[J] Math. Comput. Modelling 53, No. 9-10, 1844-1855 (2011). ISSN 0895-7177

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 2000:: *34B37 Boundary value problems with impulses
34B08 Multi-parameter boundary value problems
58E05 Abstract critical point theory
47J30 Variational methods

Keywords: impulsive; critical point; $p$-Laplacian; Sturm-Liouville boundary value problem

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