TY - JOUR

T1 - On boundary value problems for N-th order functional differential equations with impulses

AU - Domoshnitsky, Alexander

AU - Drakhlin, Michael

AU - Litsyn, Elena

N1 - Publisher Copyright:
© 1997, Razmadze Mathematical Institute. All rights reserved.

PY - 1997

Y1 - 1997

N2 - A boundary value problem is considered for an N-th order functional differential equation with impulses. It is reduced to the same boundary value problem for another equation of the same order without impulses. The reduction is based on constructing of an isomorphism between the space of the functions which are piece-wise absolutely continuous up to the (N-1)-st derivative and satisfy the impulse conditions, at the discontinuity points and the space of the functions which are absolutely continuous up to the (N-1)-st derivative. The approach allows to derive conditions on the sign preservation for the Green function of the considered boundary value problem.

AB - A boundary value problem is considered for an N-th order functional differential equation with impulses. It is reduced to the same boundary value problem for another equation of the same order without impulses. The reduction is based on constructing of an isomorphism between the space of the functions which are piece-wise absolutely continuous up to the (N-1)-st derivative and satisfy the impulse conditions, at the discontinuity points and the space of the functions which are absolutely continuous up to the (N-1)-st derivative. The approach allows to derive conditions on the sign preservation for the Green function of the considered boundary value problem.

KW - Boundary value problem

KW - Functional differential equation

KW - Green operator

KW - Isomorphism

UR - http://www.scopus.com/inward/record.url?scp=84896283702&partnerID=8YFLogxK

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AN - SCOPUS:84896283702

SN - 1512-0015

VL - 12

SP - 50

EP - 56

JO - Memoirs on Differential Equations and Mathematical Physics

JF - Memoirs on Differential Equations and Mathematical Physics

ER -