Quantum exotic: A repulsive and bottomless confining potential

On a simple model $V(x,y)=A{x}^2+B{y}^2+C{x}^2{y}^2+D(x^2{y}^4+x^4{y}^2)$ we demonstrate that even in a classically repulsive regime (i.e., at couplings which make the potential decreasing to $-\mathrm{\infty }$ in some directions) quantum mechanics may still support the purely discrete spectrum of bound states. In our example, there exists a critical boundary of this domain of stability where a further increase of repulsion causes an explosive escape of particles in infinity.