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In this paper, we study holomorphic discs in K3 surfaces and defined the openGromov-Witten invariants. Using this new invariant, we can establish a versionof correspondence between tropical discs and holomorphic discs with non-trivialinvariants. We give an example of wall-crossing phenomenon of the invariant andexpect it satisfies Kontsevich-Soibelman wall-crossing formula.

Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing