CONCENTRATION OF GROUND STATE SOLUTIONS FOR FRACTIONAL HAMILTONIAN SYSTEMS

We are concerned with the existence of ground states solutions to the following fractional Hamiltonian systems: (FHS)(lambda) {-D-t(infinity)alpha((-infinity)D(t)(alpha)u(t)) - lambda L(t)u(t) + del W (t,u(t)) = 0, u is an element of H-alpha (R, R-n), where alpha is an element of( 1/2,1), t is an element of R, u is an element of R-n, lambda > 0 is a parameter, L is an element of C (R,R-n2) is a symmetric matrix for all t is an element of R, W is an element of C-1 ( R x R-n; R) and del W (t; u) is the gradient of W ( t; u) at u. Assuming that L ( t) is a positive semi-de finite symmetric matrix for all t is an element of R, that is, L ( t) equivalent to 0 is allowed to occur in some finite interval T of R, W ( t; u) satisfies the Ambrosetti-Rabinowitz condition and some other reasonable hypotheses, we show that (FHS)(lambda) has a ground sate solution which vanishes on R \ T as lambda -> infinity, and converges to u is an element of H-alpha(R,R-n), where u is an element of E-0(alpha) is a ground state solution of the Dirichlet BVP for fractional systems on the finite interval T. Recent results are generalized and significantly improved.