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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0324-7,
author = {Irena Rach\r unkov\'a and Jan Tome\v cek},
title = {Second order BVPs with state dependent impulses via lower and upper functions},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {128-140},
zbl = {1302.34049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0324-7}
}
Irena Rachůnková; Jan Tomeček. Second order BVPs with state dependent impulses via lower and upper functions. Open Mathematics, Tome 12 (2014) pp. 128-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0324-7/
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