EXISTENCE AND NONEXISTENCE OF NONTRIVIAL SOLUTIONS FOR CHOQUARD TYPE EQUATIONS

In this article, we consider the nonlocal problem -Delta u + u = q(x) (integral(N)(R) q(y)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 (0, N), N+alpha/N < p < N+alpha/N-2 and q(x) is a given potential. Under suitable assumptions on q(x), we prove the existence and nonexistence of nontrivial solutions.