Boundary and initial value problems for second-order neutral functional differential equations

 dc.contributor.author Le, Hoan Hoa dc.contributor.author Le, Thi Phuong Ngoc dc.date.accessioned 2021-07-16T18:59:55Z dc.date.available 2021-07-16T18:59:55Z dc.date.issued 2006-05-11 dc.description.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. dc.description.department Mathematics dc.format Text dc.format.extent 19 pages dc.format.medium 1 file (.pdf) dc.identifier.citation Le, 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. dc.identifier.issn 1072-6691 dc.identifier.uri https://hdl.handle.net/10877/13935 dc.language.iso en dc.publisher Texas State University-San Marcos, Department of Mathematics dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.source Electronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. dc.subject Three-point boundary-value problem dc.subject Topological degree dc.subject Leray-Schauder nonlinear alternative dc.subject Contraction mapping principle dc.title Boundary and initial value problems for second-order neutral functional differential equations dc.type Article

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