Khalid A. Abdul-Zahra, Zeev Sobol
abstract:
In this work, we study the non-existence of a solution to an eigenvalue problem
for the Gross-Pitaevskii equation for Bose-Einstein condensation with repulsive
interaction and a trapping potential given as Borel regular measure which
vanishes at infinity in some sense. By differential equation approach, we obtain
various results on the nonexistence of the eigenvalue problem. Some celebrated
Hardy type inequalities are obtained.
Mathematics Subject Classification: 35A01, 35A23, 35D30
Key words and phrases: Bose-Einstein condensate, Hardy inequality, killing potential Technique, Pokhozhaev's test function