Abstract
In this paper, we are interested in the following Hartree system with nonlinear couplings:
where
,
,
,
,
, ε is a small parameter and
is a coupling constant, and the potentials
and
have
and
isolated global minimum points, respectively. Using the Nehari manifold technique, the energy estimate method and the Lusternik–Schnirelmann theory, we find an interesting phenomenon that the problem possesses
positive solutions when
and
do not have any common isolated global minimum points, and
positive solutions when
and
have m common isolated global minimum points. Furthermore, the existence and nonexistence of the least energy positive solutions are also explored.
2010 Mathematics Subject Classifications:
Disclosure statement
No potential conflict of interest was reported by the author(s).