R. Hakl

On a Periodic Type Boundary Value Problem for Functional Differential Equations with a Positively

abstract:
Consider the problem $$ u'(t)=H(u,u)(t)+Q(u)(t),\quad u(a)-\lambda u(b)=h(u), $$ where $H:C([a,b];R)\times C([a,b];R)\to L([a,b];R)$ is a continuous positively homogeneous operator, $Q:C([a,b];R)\to L([a,b];R)$ is a continuous operator satisfying the Carath\'eodory condition, $h:C([a,b];R)\to R$ is a continuous functional, and $\lambda\in[0,1[\,$. The efficient conditions sufficient for the existence of a solution to the problem considered are established.

Mathematics Subject Classification: 34K10

Key words and phrases: Boundary value problem, functional differential equation, solvability