Ground state homoclinic orbits of damped vibration problems

摘要

In this paper, we consider a class of non-periodic damped vibration problems with superquadratic nonlinearities. We study the existence of nontrivial ground state homoclinic orbits for this class of damped vibration problems under some conditions weaker than those previously assumed. To the best of our knowledge, there has been no work focused on this case. MSC: 49J40, 70H05.