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In this work, we study the higher order Kirchhoff type Choquard equation$(KC)$ involving a critical exponential non-linearity and singular weights. Weprove the existence of solution to $(KC)$ using Mountain pass Lemma in light ofMoser-Trudinger and singular Adams-Moser inequalities. In the second part ofthe paper, using the Nehari manifold technique and minimization over itssuitable subsets, we prove the existence of at least two solutions to theKirchhoff type Choquard equation $(\mathcal{P_{\la,M}})$ involvingconvex-concave type non-linearity.

Polyharmonic Kirchhoff problems involving exponential non-linearity of Choquard type with singular weights