Boundary and initial value problems for second-order neutral functional differential equations
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Date
2006-05-11
Authors
Le, Hoan Hoa
Le, Thi Phuong Ngoc
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
In this paper, we consider the three-point boundary-value problem for the second order neutral functional differential equation
u″ + ƒ(t, ut, u′(t)) = 0, 0 ≤ t ≤ 1,
with the three-point boundary condition u0 = ϕ, u(1) = u(η). Under suitable assumptions on the function ƒ 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 u0 = ϕ, u(1) = α[u′(η) - u′(0)], or with an initial condition u0 = 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.
Description
Keywords
Three-point boundary-value problem, Topological degree, Leray-Schauder nonlinear alternative, Contraction mapping principle
Citation
Le, H. H., & Le, T. P. N. (2006). Boundary and initial value problems for second-order neutral functional differential equations. <i>Electronic Journal of Differential Equations, 2006</i>(62), pp. 1-19.
Rights
Attribution 4.0 International