TY - JOUR

T1 - The sturm separation theorem for impulsive delay differential equations

AU - Domoshnitsky, Alexander

AU - Raichik, Vladimir

N1 - Publisher Copyright:
© 2018 Alexander Domoshnitsky et al., published by Sciendo.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - Sturm separation theorem

KW - Wronskian

KW - delay differential equations

UR - http://www.scopus.com/inward/record.url?scp=85061445394&partnerID=8YFLogxK

U2 - 10.2478/tmmp-2018-0006

DO - 10.2478/tmmp-2018-0006

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AN - SCOPUS:85061445394

SN - 1210-3195

VL - 71

SP - 65

EP - 70

JO - Tatra Mountains Mathematical Publications

JF - Tatra Mountains Mathematical Publications

IS - 1

ER -