  We consider confinement of Dirac fermions in $AB$-stacked bilayer graphene by
inhomogeneous on-site interactions, (pseudo-)magnetic field or inter-layer
interaction. Working within the framework of four-band approximation, we focus
on the systems where the stationary equation is reducible into two stationary
equations with $2\times2$ Dirac-type Hamiltonians and auxiliary interactions.
We show that it is possible to find localized states by solving an effective
Schr\"odinger equation with energy-dependent potential. We consider several
scenarios where bilayer graphene is subject to inhomogneous (pseudo-)magnetic
field, on-site interactions or inter-layer coupling. In explicit examples, we
provide analytical solutions for the states localized by local fluctuations or
periodicity defects of the interactions.
