Chengjun Guo, Donal O'Regan, Chengjiang Wang, and Ravi P. Agarwal

Periodic Solutions of Superquadratic Nonautonomous Differential Systems with a Delay

The nonautonomous delay differential system
$$ x^{\prime}(t)=f(t, x(t-\tau)), $$
is considered, where $\tau>0$, $f:R\times R^n\to R^n$ is a continuous vector function such that
$$ f(t+4\tau,x)=f(t,x), \quad f(t,x)=\nabla_xF(t,x). $$
Using the critical point theory, the conditions ensuring the existence of a nontrivial $4\tau$-periodic solution of that system are established in the case, where $F(t,x)$ is superquadratic in $x$.

Mathematics Subject Classification: 34K13, 34K18, 58E50

Key words and phrases: Delay differential equations, critical point theory, linking theorem, superquadratic growth condition