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. <i>Electronic Journal of Differential Equations, 2006</i>(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 |