MMN-21
On periodic-type boundary value problems for functional differential equations with positively homogeneous operator
Abstract
Consider the problem
$$
u'(t)=H(u)(t)+Q(u)(t),\qquad u(a)-\lambda u(b)=h(u),
$$
where $H,Q:C([a,b];\mathbb{R})\to L([a,b];\mathbb{R})$ are
continuous operators satisfying the Carath\`eodory condition, the
operator $H$ is positively homogeneous, $\lambda\in \mathbb{R}_+$,
and $h:C([a,b];\mathbb{R})\to \mathbb{R}$ is a continuous
functional. In this paper, efficient sufficient conditions
guaranteeing the solvability and unique solvability of the problem
considered are established.
Vol. 5 (2004), No. 1, pp. 33-55