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The existence of a deep western boundary current (DWBC) in the South China Sea (SCS) was verified by direct observations from three current moorings deployed from September 2015 to September 2018. The average current speeds observed in the DWBC were around 1cm/s along the northern boundary and 3cm/s along the western boundary. The DWBC demonstrates significant intraseasonal variability in the 30-120 days period band, which may come from the variability in the Luzon overflow or the eddies in the deep SCS forced by a stable Luzon overflow. In addition, observations found that this DWBC along the northern boundary can reverse its direction meridionally in the spring. Model results suggest that if the Luzon overflow decreases 1/3 of its typical transport, this current reversal can occur. This behavior can be explained through ‘relaxation’ theory.

This paper is devoted to study the following third-order multi-point singularly perturbed boundary value problemwhere a, b, c, d 0, A, B ∈ R, a + b > 0, c + d > 0, i 0, i 0, i = 1, 2, . . . , n − 2, 0 < 1 < 2 < · · · < n−2 < 1, and 0 < 1 < 2 < · · · < n−2 < 1. The existence, uniqueness and asymptotic estimates of solutions of the boundary value problem are give by using priori estimates, differential inequalities technique and Leray-Schauder degree theory.

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