A.  Lomtatidze and P. Vodstrčil

On Solvability of a Three-Point Boundary Value Problem for Second Order Nonlinear Functional Differential Equations

abstract:
Sufficient conditions for the solvability of the problem $$ u''(t) = \ell (u)(t) + F(u)(t); \;\;\; u(a)=0, \;\; u(b)=u(t_0) $$ are established, where $t_0 \in \,]a,b[\,$, $\ell,F:C([a,b];\mathbb{R})\to L([a,b];\mathbb{R})$ are continuous operators, and $\ell$ is linear.

Mathematics Subject Classification: 34K06, 34K10

Key words and phrases: second order nonlinear functional differential equation, three-point BVP