# 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

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topDomoshnitsky, 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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