Classification of integrable representations for toroidal extended affine Lie algebras

In this paper, we classify the irreducible integrable modules with finite dimensional weight spaces and non-trivial $\widetilde{\mathfrak g}_c$-action for the nullity $2$ toroidal extended affine Lie algebra $\widetilde{\mathfrak g}$, where $\widetilde{\mathfrak g}_c$ is the core of $\widetilde{\mathfrak g}$.