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

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.

Keywords

• Eigenvalues
• bifurcation technique
• global behavior
• multiple solutions