Existence results for non-trivial solutions to singular elliptic equations via variational methods

This research investigates the existence of non-trivial weak solutions for a class of singular elliptic boundary value problems featuring general divergence-form differential operators. The analytical approach employs modern variational techniques combined with critical point theory, utilizing two fundamental existence theorems from nonlinear analysis. The developed framework demonstrates that under appropriate conditions, such singular problems admit at least one non-trivial weak solution. The methodology presented here extends classical variational principles to handle the singular nature of the considered differential equations.