About differential inequalities for nonlocal boundary value problems with impulsive delay equations

Alexander Domoshnitsky; Irina Volinsky

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 2, page 121-128
  • ISSN: 0862-7959

Abstract

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We propose results about sign-constancy of Green's functions to impulsive nonlocal boundary value problems in a form of theorems about differential inequalities. One of the ideas of our approach is to construct Green's functions of boundary value problems for simple auxiliary differential equations with impulses. Careful analysis of these Green's functions allows us to get conclusions about the sign-constancy of Green's functions to given functional differential boundary value problems, using the technique of theorems about differential and integral inequalities and estimates of spectral radii of the corresponding compact operators in the space of essential bounded functions.

How to cite

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Domoshnitsky, Alexander, and Volinsky, Irina. "About differential inequalities for nonlocal boundary value problems with impulsive delay equations." Mathematica Bohemica 140.2 (2015): 121-128. <http://eudml.org/doc/271603>.

@article{Domoshnitsky2015,
abstract = {We propose results about sign-constancy of Green's functions to impulsive nonlocal boundary value problems in a form of theorems about differential inequalities. One of the ideas of our approach is to construct Green's functions of boundary value problems for simple auxiliary differential equations with impulses. Careful analysis of these Green's functions allows us to get conclusions about the sign-constancy of Green's functions to given functional differential boundary value problems, using the technique of theorems about differential and integral inequalities and estimates of spectral radii of the corresponding compact operators in the space of essential bounded functions.},
author = {Domoshnitsky, Alexander, Volinsky, Irina},
journal = {Mathematica Bohemica},
keywords = {impulsive equation; nonlocal boundary value problem; Green's function; positivity of Green's function; negativity of Green's function; estimates of solutions},
language = {eng},
number = {2},
pages = {121-128},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {About differential inequalities for nonlocal boundary value problems with impulsive delay equations},
url = {http://eudml.org/doc/271603},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Domoshnitsky, Alexander
AU - Volinsky, Irina
TI - About differential inequalities for nonlocal boundary value problems with impulsive delay equations
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 2
SP - 121
EP - 128
AB - We propose results about sign-constancy of Green's functions to impulsive nonlocal boundary value problems in a form of theorems about differential inequalities. One of the ideas of our approach is to construct Green's functions of boundary value problems for simple auxiliary differential equations with impulses. Careful analysis of these Green's functions allows us to get conclusions about the sign-constancy of Green's functions to given functional differential boundary value problems, using the technique of theorems about differential and integral inequalities and estimates of spectral radii of the corresponding compact operators in the space of essential bounded functions.
LA - eng
KW - impulsive equation; nonlocal boundary value problem; Green's function; positivity of Green's function; negativity of Green's function; estimates of solutions
UR - http://eudml.org/doc/271603
ER -

References

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