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dc.contributor.authorLe, Hoan Hoa ( )
dc.contributor.authorLe, Thi Phuong Ngoc ( )
dc.identifier.citationLe, H. H., & Le, T. P. N. (2006). Boundary and initial value problems for second-order neutral functional differential equations. Electronic Journal of Differential Equations, 2006(62), pp. 1-19.en_US

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.

dc.format.extent19 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectThree-point boundary-value problemen_US
dc.subjectTopological degreeen_US
dc.subjectLeray-Schauder nonlinear alternativeen_US
dc.subjectContraction mapping principleen_US
dc.titleBoundary and initial value problems for second-order neutral functional differential equationsen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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