Electron. J. Diff. Equ., Vol. 2013 (2013), No. 171, pp. 1-14.

Global properties and multiple solutions for boundary-value problems of impulsive differential equations

Jing Wang, Baoqiang Yan

Abstract:
This article presents global properties and existence of multiple solutions for a class of boundary value problems of impulsive differential equations. We first show that the spectral properties of the linearization of these problems are similar to the well-know properties of the standard Sturm-Liouville problems. These spectral properties are then used to prove two Rabinowitz-type global bifurcation theorems. Finally, we use the global bifurcation theorems to obtain multiple solutions for the above problems having specified nodal properties.

Submitted June 4, 2013. Published July 26, 2013.
Math Subject Classifications: 34B09, 34B15, 34B37.
Key Words: Eigenvalues; bifurcation technique; global behavior; multiple solutions.

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Jing Wang
School of Mathematical Sciences, Shandong Normal University
Jinan, 250014, China
email: wnself36@gmail.com
Baoqiang Yan
School of Mathematical Sciences, Shandong Normal University
Jinan, 250014, China
email: yanbaoqiang666@gmail.com

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