On a Class of Choquard‐Kirchhoff Problems Involving a Generalized Double‐Phase Operator

ABSTRACT In this paper, we establish existence results for a class of Choquard‐Kirchhoff problems driven by double‐phase operators with gradient‐dependent exponents. Particular attention is devoted to the analysis of the associated nonlinear differential operator, where we investigate key structural properties such as boundedness, continuity, strict monotonicity, and the ‐property condition. These properties play a fundamental role in the construction of an appropriate functional framework and allow the application of the Berkovits topological degree theory. As a consequence, we obtain the existence of weak solutions to the considered problem.