  We address the resonant response and bistability of the exciton-polariton
corner states in a higher-order nonlinear topological insulator realized with
kagome arrangement of microcavity pillars. Such states are resonantly excited
and exist due to the balance between pump and losses, on the one hand, and
between nonlinearity and dispersion in inhomogeneous potential landscape, on
the other hand, for pump energy around eigen-energies of corresponding linear
localized modes. Localization of the nonlinear corner states in a higher-order
topological insulator can be efficiently controlled by tuning pump energy. We
link the mechanism of corner state formation with symmetry of the truncated
kagome array. Corner states coexist with densely packed edge states, but are
well-isolated from them in energy. Nonlinear corner states persist even in the
presence of perturbations in corner microcavity pillar.
