A note on a class of noncoercive functionals

Abstract Our goal here is to prove the existence of a nontrivial critical point to the following functional: I(u) = 1 p ‖Du‖ p p − ∫ ω |u| p ln (1 + u 2 ) . by using the well-known Mountain-Pass theorem with the Ceramil Palais-Smale condition.