Existence and Blow Up Behavior of Prescribed Mass Solutions on Large Smooth Domains to the Kirchhoff Equation With Combined Nonlinearities

ABSTRACT In this paper, we consider the existence, multiplicity, and the asymptotic behavior of solutions with prescribed mass for the following nonlinear Kirchhoff equation with mixed nonlinearities: where is a large bounded smooth star‐shaped domain or the whole space , , and is the potential. The standard approach based on the Pohozaev identity for obtaining normalized solutions becomes inapplicable in this setting due to the presence of the potential . When , we perform a detailed blow‐up analysis to describe the asymptotic behavior of such solutions as . Furthermore, for and , we also prove that is a bifurcation point in the case .