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

Tsamatos, P. Ch.; Ntouyas, S. K.

Int. J. Math. Math. Sci. 19, No. 2, 335-342 (1996).

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 \((*)\).

Reviewer: T.Dłotko (Katowice)

MSC:

34K10

Boundary value problems for functional-differential equations

Keywords:

boundary value problem