Nagumo type existence results of Sturm–Liouville BVP for impulsive differential equations

In this paper, the method of upper and lower solutions and the Schauder degree theory are employed in the study of Sturm–Liouville boundary value problems for second order impulsive differential equations. We obtain the existence of at least three solutions to the problem under the assumption that t...

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Bibliographic Details
Published in:Nonlinear analysis 2011-12, Vol.74 (17), p.6676-6685
Main Authors: Liang, Ruixi, Liu, Zaiming
Format: Article
Language:English
Subjects:
Boundary value problem
Boundary value problems
Derivatives
Differential equations
Exact sciences and technology
Impulse
Mathematical analysis
Mathematics
Nagumo condition
Nonlinearity
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations, boundary value problems
Sciences and techniques of general use
Upper and lower solutions
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Summary:In this paper, the method of upper and lower solutions and the Schauder degree theory are employed in the study of Sturm–Liouville boundary value problems for second order impulsive differential equations. We obtain the existence of at least three solutions to the problem under the assumption that the nonlinear term f satisfies a Nagumo condition with respect to the first order derivative.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2011.06.047