GROUND STATE SOLUTIONS FOR CHOQUARD TYPE EQUATIONS WITH A SINGULAR POTENTIAL

This article concerns the Choquard type equation -Delta u+v(x)u = ( integral N-R vertical bar u(y)vertical bar p/ vertical bar x - y vertical bar(N-alpha)dy ) vertical bar u vertical bar(p-2)u, x is an element of R-N where N >= 3, alpha is an element of ((N - 4)+,N), 2 <= p < (N + alpha)/(N - 2) and V(x) is a possibly singular potential and may be unbounded below. Applying a variant of the Lions' concentration-compactness principle, we prove the existence of ground state solution of the above equations.