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Bifurcation of positive periodic solutions of first-order impulsive differential equations

Ruyun Ma*, Bianxia Yang and Zhenyan Wang

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Department of Mathematics, Northwest Normal University, Lanzhou, 730070, P.R. China

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Boundary Value Problems 2012, 2012:83 doi:10.1186/1687-2770-2012-83

Published: 1 August 2012

Abstract

We give a global description of the branches of positive solutions of first-order impulsive boundary value problem:

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/83/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/83/mathml/M1">View MathML</a>

which is not necessarily linearizable. Where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/83/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/83/mathml/M2">View MathML</a> is a parameter, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/83/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/83/mathml/M3">View MathML</a> are given impulsive points. Our approach is based on the Krein-Rutman theorem, topological degree, and global bifurcation techniques.

MSC: 34B10, 34B15, 34K15, 34K10, 34C25, 92D25.

Keywords:
Krein-Rutman theorem; topological degree; bifurcation from interval; impulsive boundary value problem; existence and multiplicity