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Bai, Liang; Dai, Binxiang

Existence and multiplicity of solutions for an impulsive boundary value problem with a parameter via critical point theory. (English) Zbl 1219.34039

Math. Comput. Modelling 53, No. 9-10, 1844-1855 (2011).
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.

Cited in 24 Documents

MSC:

34B37 Boundary value problems with impulses for ordinary differential equations
34B08 Parameter dependent boundary value problems for ordinary differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
47J30 Variational methods involving nonlinear operators

Keywords:

impulsive; critical point; \(p\)-Laplacian; Sturm-Liouville boundary value problem
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\textit{L. Bai} and \textit{B. Dai}, Math. Comput. Modelling 53, No. 9--10, 1844--1855 (2011; Zbl 1219.34039)
Full Text: DOI

References:

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