ABSTRACT
In this paper, we develop a direct approach to find Nehari-type ground state solutions for the following Schrödinger equation with inverse square potential and critical Sobolev exponent
where
,
(the critical Sobolev exponent),
,
and
. Under the conditions
and
and some other mild assumptions on V and f, we prove the existence of a positive ground state solution of Nehari-type to the above problem in the asymptotically periodic case and asymptotically constant case, respectively, with
satisfying
for some
.
COMMUNICATED BY:
Disclosure statement
No potential conflict of interest was reported by the authors.