Geodesic
Initial value problems for nonlinear nonresonant delay differential equations with possibly infinite delay
Electronic journal of differential equations, Tome 1997 (1997)
We study initial value problems for scalar, nonlinear, delay differential equations with distributed, possibly infinite, delays. We consider the initial value problem $\varphi$ and $f$ are bounded and $\mu$ is a finite Borel measure. Motivated by the nonresonance condition for the linear case and previous work of the authors, we introduce conditions on $g$. Under these conditions, we prove an existence and uniqueness theorem. We show that under the same conditions, the solutions are globally asymptotically stable and, if $\mu$ satisfies an exponential decay condition, globally exponentially asymptotically stable.
Classification : 34K05, 34K20, 34K25
Keywords: delay differential equation, infinite delay, initial value problem, nonresonance, asymptotic stability, exponential asymptotic stability 
@article{EJDE_1997__1997__a38,
     author = {Drager,  Lance D. and Layton,  William},
     title = {Initial value problems for nonlinear nonresonant delay differential equations with possibly infinite delay},
     journal = {Electronic journal of differential equations},
     year = {1997},
     volume = {1997},
     zbl = {0889.34056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a38/}
}
TY  - JOUR
AU  - Drager,  Lance D.
AU  - Layton,  William
TI  - Initial value problems for nonlinear nonresonant delay differential equations with possibly infinite delay
JO  - Electronic journal of differential equations
PY  - 1997
VL  - 1997
UR  - http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a38/
LA  - en
ID  - EJDE_1997__1997__a38
ER  - 
%0 Journal Article
%A Drager,  Lance D.
%A Layton,  William
%T Initial value problems for nonlinear nonresonant delay differential equations with possibly infinite delay
%J Electronic journal of differential equations
%D 1997
%V 1997
%U http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a38/
%G en
%F EJDE_1997__1997__a38
Drager,  Lance D.; Layton,  William. Initial value problems for nonlinear nonresonant delay differential equations with possibly infinite delay. Electronic journal of differential equations, Tome 1997 (1997). http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a38/