  We demonstrate the existence of confined states in one- and two-dimensional
(1D and 2D) systems of two linearly-coupled components, with the confining
harmonic-oscillator (HO) potential acting upon one component, and an expulsive
anti-HO potential acting upon the other. The systems ca be implemented in
optical and BEC dual-core waveguides. In the 1D linear system, codimension-one
solutions are found in an exact form for the ground state (GS) and dipole mode
(the first excited state). Generic solutions are produced by means of the
variational approximation, and are found in a numerical form. Exact
codimension-one solutions and generic numerical ones are also obtained for the
GS and vortex states in the 2D system (the exact solutions are found for all
values of the vorticity). Both the trapped and anti-trapped components of the
bound states may be dominant ones, in terms of the norm. The localized modes
may be categorized as bound states in continuum, as they coexist with
delocalized ones. The 1D states, as well as the GS in 2D, are weakly affected
and remain stable if the self-attractive or repulsive nonlinearity is added to
the system. The self-attraction makes the vortex states unstable against
splitting, while they remain stable under the action of the self-repulsion.
