On a boundary value problem on an infinite interval for nonlinear functional differential equations

Sufficient conditions are found for the solvability of the following boundary value problem:u^{(n)}(t)=f(u)(t),\qquad u^{(i-1)}(0)=\varphi_{i}(u^{(n-1)}(0))\quad(i=1,% \dots,n-1),\qquad\liminf_{t\to+\infty}\lvert u^{(n-2)}(t)|<+\infty,where {f\colon C^{n-1}(\mathbb{R}_{+})\to L_{\mathrm{loc}}(\mathbb{R}_{+})} is a continuous Volterra operator, and {\varphi_{i}\colon\mathbb{R}\to\mathbb{R}} ({i=1,\dots,n}) are continuous functions.