Existence of critical point for abstract resonant problems with unbounded nonlinearities and applications to differential equations

In this paper, using well-known variational methods, we prove a general abstract theorem on the existence of a critical point for resonant problems with unbounded nonlinearities and then apply it to ordinary and partial differential equations with generalized Ahmad–Lazer–Paul conditions. The abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations.