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

1994
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Bulletin of the Australian Mathematical Society
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Let / be a real function denned on [0, l]xR s and let r\ e (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 r x" = f (t, x, x 1 , x") (Theorem 1 and Remark 4 of [Nonlinear Anal. 16 (1991), 949-957]). The aim of the present paper is simply to point out how, by means of a completely different approach, it is possible to improve that result not only by

doi:10.1017/s0004972700016014
fatcat:imndmzf4g5bejdsxk3lyum4jai