Mattar, Rebecca
(2019-12-14)
The aim of this thesis is to study the qualitative behavior of a specific non-linear Volterra integro-differential equation with finite delays by using Lyapunov's second method. The non-linear Volterra integro-differential equation is:
$x'(t)=b(t)x(t-r_1)-\int_{t-r_2}^{t}a(t,s)g(x(s))ds,$
where $r_1$, $r_2$ are positive constants representing 2 finite delays, $t \geq 0$ and
$a : \ [0,\infty) \times [-\tau, \infty) \rightarrow \R, \qquad \text{and} \qquad b : \ [0, \infty ) \rightarrow \R$
are two continuous functions.
In the first part, we study the qualitative behavior of the constant ...