Abstract
We study the Schrödinger equation:Section.Display where
is periodic and
is periodic in the
-variables,
is in a gap of the spectrum of the operator
and
is asymptotically linear as
We prove that under some asymptotically linear assumptions for
, this equation has a nontrivial solution. Our assumptions for
are different from the classical assumptions raised by Li and Szulkin.
Acknowledgments
The authors would like to thank the anonymous referees for their comments and suggestions on the manuscript. Shaowei Chen was supported by Science Foundation of Huaqiao University and Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University.