# Second order BVPs with state dependent impulses via lower and upper functions

Open Mathematics (2014)

• Volume: 12, Issue: 1, page 128-140
• ISSN: 2391-5455

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## Abstract

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The paper deals with the following second order Dirichlet boundary value problem with p ∈ ℕ state-dependent impulses: z″(t) = f (t,z(t)) for a.e. t ∈ [0, T], z(0) = z(T) = 0, z′(τ i+) − z′(τ i−) = I i(τ i, z(τ i)), τ i = γ i(z(τ i)), i = 1,..., p. Solvability of this problem is proved under the assumption that there exists a well-ordered couple of lower and upper functions to the corresponding Dirichlet problem without impulses.

## How to cite

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Irena Rachůnková, and Jan Tomeček. "Second order BVPs with state dependent impulses via lower and upper functions." Open Mathematics 12.1 (2014): 128-140. <http://eudml.org/doc/269759>.

@article{IrenaRachůnková2014,
abstract = {The paper deals with the following second order Dirichlet boundary value problem with p ∈ ℕ state-dependent impulses: z″(t) = f (t,z(t)) for a.e. t ∈ [0, T], z(0) = z(T) = 0, z′(τ i+) − z′(τ i−) = I i(τ i, z(τ i)), τ i = γ i(z(τ i)), i = 1,..., p. Solvability of this problem is proved under the assumption that there exists a well-ordered couple of lower and upper functions to the corresponding Dirichlet problem without impulses.},
author = {Irena Rachůnková, Jan Tomeček},
journal = {Open Mathematics},
keywords = {Impulsive differential equation; State-dependent impulses; Upper and lower functions method; Upper and lower solutions method; Dirichlet problem; Second order ODE; impulsive differential equation; state dependent impulses; upper and lower functions method; upper and lower solutions methos; second order ODE},
language = {eng},
number = {1},
pages = {128-140},
title = {Second order BVPs with state dependent impulses via lower and upper functions},
url = {http://eudml.org/doc/269759},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Irena Rachůnková
AU - Jan Tomeček
TI - Second order BVPs with state dependent impulses via lower and upper functions
JO - Open Mathematics
PY - 2014
VL - 12
IS - 1
SP - 128
EP - 140
AB - The paper deals with the following second order Dirichlet boundary value problem with p ∈ ℕ state-dependent impulses: z″(t) = f (t,z(t)) for a.e. t ∈ [0, T], z(0) = z(T) = 0, z′(τ i+) − z′(τ i−) = I i(τ i, z(τ i)), τ i = γ i(z(τ i)), i = 1,..., p. Solvability of this problem is proved under the assumption that there exists a well-ordered couple of lower and upper functions to the corresponding Dirichlet problem without impulses.
LA - eng
KW - Impulsive differential equation; State-dependent impulses; Upper and lower functions method; Upper and lower solutions method; Dirichlet problem; Second order ODE; impulsive differential equation; state dependent impulses; upper and lower functions method; upper and lower solutions methos; second order ODE
UR - http://eudml.org/doc/269759
ER -

## References

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