BOUNDARY AND INITIAL VALUE PROBLEMS FOR SECOND-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Hoa Hoan, Thi Le, Ngoc Phuong, Le
2006 Electronic Journal of Differential Equations   unpublished
In this paper, we consider the three-point boundary-value problem for the second order neutral functional differential equation u + f (t, ut, u (t)) = 0, 0 ≤ t ≤ 1, with the three-point boundary condition u 0 = φ, u(1) = u(η). Under suitable assumptions on the function f we prove the existence, uniqueness and continuous dependence of solutions. As an application of the methods used, we study the existence of solutions for the same equation with a "mixed" boundary condition u 0 = φ, u(1) = α[u
more » ... ) − u (0)], or with an initial condition u 0 = φ, u (0) = 0. For the initial-value problem, the uniqueness and continuous dependence of solutions are also considered. Furthermore, the paper shows that the solution set of the initial-value problem is nonempty, compact and connected. Our approach is based on the fixed point theory.
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