## Some results on boundary value problems for functional differential equations.(English)Zbl 0847.34074

The boundary value problem $$(*)$$ $$x''(t)+ f(t, x_t, x'(t))= 0$$, $$t\in [0, T]$$, $$a_0 x_0- b_0 x' (0)= \varphi$$, $$c_0 x(T)+ d_0 x' (T)= \eta$$, $$x_0= x(\theta)$$, $$\theta\in [-r, 0]$$, $$\varphi\in \mathbb{C}$$, $$\eta\in \mathbb{R}^n$$, is considered. Using a priori estimates and the nonlinear alternative of Leray-Schauder the existence of at least one solution to $$(*)$$ is demonstrated. The result is a generalization of a recent one for ODE and completes an earlier one on the same problem $$(*)$$.

### MSC:

 34K10 Boundary value problems for functional-differential equations

### Keywords:

boundary value problem
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