Standing wave solutions of the discrete non-linear Schrödinger equations with unbounded potentials, II

Abstract

In this article, we prove the existence of infinitely many non-trivial standing wave solutions of the discrete non-linear Schrödinger equation with the unbounded potential at infinity by using the linking theorem.

Keywords:

• discrete non-linear Schrödinger equation
• standing wave solution
• Palais–Smale condition
• linking theorem

AMS Subject Classifications::

• 35Q55
• 35Q51
• 37L60
• 39A12
• 39A70
• 47J30
• 78A40