R\'esolution du $\mathrm{\partial }\bar{\mathrm{\partial }}$ pour les courants prolongeables d\'efinis sur un domaine pseudoconvexe non born\'e de ${\mathbb{C}}^n$

In this present paper, we solve the $\mathrm{\partial }\bar{\mathrm{\partial }}$ for extendable currents definite in a pseudoconvexe unbounded domain of ${\mathbb{C}}^n$ .