Abstract
Here, first we shall find connections between the solutions of the initial value problem (6.1), and its perturbed system (6.2) satisfying, instead of the same initial condition y(k 0) = x 0, the m-point boundary conditions
where k 0 ≤ k 1 ≤ k 2 ⋯ ≤ k m ≤ k 0 + J, k i ∈ I 0,J = {k 0, k 0 + 1, ⋯ , k 0 + J}, A i ∈ ℝn ×n, i = 1, 2, ⋯ , m are constant matrices, and γ ∈ ℝ n is a constant vector. Then, these connections will be used to study the existence and uniqueness of the solutions of the boundary value problem (6.2), (33.1) in ‘generalized (vector) normed spaces’. An iterative scheme which can be used to compute approximate solutions of (6.2), (33.1) will also be provided. In what follows, it is sufficient to assume that the systems (6.1) and (6.2) are defined only on I0,J . We begin with the following:
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© 1997 Springer Science+Business Media Dordrecht
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Agarwal, R.P., Wong, P.J.Y. (1997). Solutions of m-Point Boundary Value Problems. In: Advanced Topics in Difference Equations. Mathematics and Its Applications, vol 404. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8899-7_33
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DOI: https://doi.org/10.1007/978-94-015-8899-7_33
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4839-4
Online ISBN: 978-94-015-8899-7
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