<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Wronskian is one of the classical objects in the theory of ordinary differential equations. Properties of Wronskian lead to important conclusions on behaviour of solutions of delay equations. For instance, non-vanishing Wronskian ensures validity of the Sturm separation theorem (between two adjacent zeros of any solution there is one and only one zero of every other nontrivial linearly independent solution) for delay equations. We propose the Sturm separation theorem in the case of impulsive delay differential equations and obtain assertions about its validity.</p></abstract>

Wronskian is one of the classical objects in the theory of ordinary differential equations. Properties of Wronskian lead to important conclusions on behaviour of solutions of delay equations. For instance, non-vanishing Wronskian ensures validity of the Sturm separation theorem (between two adjacent zeros of any solution there is one and only one zero of every other nontrivial linearly independent solution) for delay equations. We propose the Sturm separation theorem in the case of impulsive delay differential equations and obtain assertions about its validity.

The Sturm Separation Theorem for Impulsive Delay Differential Equations

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"The Sturm Separation Theorem for Impulsive Delay Differential Equations"}

Wronskian is one of the classical objects in the theory of ordinary differential equations. Properties of Wronskian lead to important conclusions on behaviour...

The Sturm Separation Theorem for Impulsive Delay Differential Equations

Published Online: Jan 25, 2019

Page range: 65 - 70

Received: Nov 12, 2017

DOI: https://doi.org/10.2478/tmmp-2018-0006

Keywords
delay differential equations, Sturm separation theorem, Wronskian

© 2018 Alexander Domoshnitsky et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Sturm Separation Theorem for Impulsive Delay Differential Equations

Published Online: Jan 25, 2019

Page range: 65 - 70

Received: Nov 12, 2017

DOI: https://doi.org/10.2478/tmmp-2018-0006

Keywordsdelay differential equations, Sturm separation theorem, Wronskian

© 2018 Alexander Domoshnitsky et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
delay differential equations, Sturm separation theorem, Wronskian