The authors of this very interesting paper consider the nonlinear Schrödinger equation having the form
for , where as . This equation arises in numerous applications in physics and chemistry. It turns out that there exist infinitely many homoclinic type solutions under the following assumptions:
(1) , and is 1-periodic in ;
(2) and is 1-periodic in ;
(3) and , for ;
(4) , as uniformly in , where is 1-periodic in and inf ;
(5) and there is such that whenever .
Then there exist infinitely many -distinct solutions. Here two solutions of the equation under consideration are said to be geometrically distinct (or -distinct) if for all , where . The second result concerns the case under assumptions (1)-(3) and a modification of (4) and (5). Then the authors prove again that there exist infinitely many -distinct solutions.