Summary
For a discrete analogy with n − 1 ∈ N grid points of a nonlinear ordinary boundary-value problem with an implicit differential equation of the second order, the existence of 2n−1−2 extraneus solutions is shown, whose sequences of difference quotients of the first and the second order are uniformly bounded as n → ∞. For selected explicitly represented sequences of extraneous solutions, the limiting function as n → ∞ is explicitly given. These functions either do not solve the differential equatin or only in a non-classical sense.
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References
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This paper is dedicated to Professor Dr. J. Weissinger on the occasion of his 70th birthday.
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Spreuer, H., Adams, E. On extraneous solutions with uniformly bounded difference quotients for a discrete analogy of a nonlinear ordinary boundary-value problem. J Eng Math 19, 45–55 (1985). https://doi.org/10.1007/BF00055040
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DOI: https://doi.org/10.1007/BF00055040