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In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term [...] τ(u(t))=a+bu(t)c+bu(t). Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.
Sertaç Erman, and Ali Demir. "An analysis on the stability of a state dependent delay differential equation." Open Mathematics 14.1 (2016): 425-435. <http://eudml.org/doc/285500>.
@article{SertaçErman2016, abstract = {In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term [...] τ(u(t))=a+bu(t)c+bu(t).$\tau (u(t)) = \frac\{\{a + bu(t)\}\}\{\{c + bu(t)\}\}.$ Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.}, author = {Sertaç Erman, Ali Demir}, journal = {Open Mathematics}, keywords = {Asymptotic stability; state depended delay; delay differential equation; asymptotic stability; state dependent delay; existence and uniqueness}, language = {eng}, number = {1}, pages = {425-435}, title = {An analysis on the stability of a state dependent delay differential equation}, url = {http://eudml.org/doc/285500}, volume = {14}, year = {2016}, }
TY - JOUR AU - Sertaç Erman AU - Ali Demir TI - An analysis on the stability of a state dependent delay differential equation JO - Open Mathematics PY - 2016 VL - 14 IS - 1 SP - 425 EP - 435 AB - In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term [...] τ(u(t))=a+bu(t)c+bu(t).$\tau (u(t)) = \frac{{a + bu(t)}}{{c + bu(t)}}.$ Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation. LA - eng KW - Asymptotic stability; state depended delay; delay differential equation; asymptotic stability; state dependent delay; existence and uniqueness UR - http://eudml.org/doc/285500 ER -