Abstract
The existence of multi-bump solutions for the following class of quasilinear Schrödinger equations in
is established, where
and h is a continuous function,
are continuous functions verifying some hypotheses. By a change of variables, the quasilinear equations are reduced to a semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem for suitable assumptions. We show that if the zero set of V(x) has several isolated connected components
such that the interior of
is not empty and
is smooth, then for
large there exists, for any non-empty subset
, a bump solution which is trapped in a neighbourhood of
.
Notes
No potential conflict of interest was reported by the authors.