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A remark on a third-order three-point boundary value problem

Published online by Cambridge University Press:  17 April 2009

Salvatore A. Marano
Salvatore A. Marano
Affiliation:
Dipartimento di Matematica Città, Universitaria Viale, A. Doria 6, 95125 Catania, Italy
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Abstract

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Let f be a real function defined on [0, 1] × R3 and let η ∈ (0, 1). Very recently, C.P. Gupta and V. Lakshimikantham, making use of the Leray-Schauder continuation theorem and Wirtinger-type inequalities, established an existence result for the problem

(Theorem 1 and Remark 4 of [Nonlinear Anal. 16 (1991), 949–957]).

The aim of the present paper is simply to point out how, bu means of a completely different approach, it is possible to improve that result not only by requiring much general on f, but also by giving a precise pointwise estimate on x″′

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 1 , February 1994 , pp. 1 - 5
Copyright
Copyright © Australian Mathematical Society 1994

References

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[3]Gupta, C.P. and Lakshmikantham, V., ‘Existence and uniqueness theorems for a third-order three-point boundary value problem’, Nonlinear Anal. 16 (1991), 949–957.Google Scholar
[4]Köthe, G., Topological vector spaces-I (Springer-Verlag, Berlin, Heidelberg, New York, 1969).Google Scholar