Existence Results for a Class of Nonlocal p -Laplacian Equations

In this paper, we focus our attention on the nonlocal equation { − div ( a ( x ) | ∇ u | p − 2 ∇ u ) + η ψ ( x ) ∫ Ω φ u = f ( x , u ) , in Ω , u = 0 , on ∂ Ω , getting nontrivial weak solutions for some classes of functions f , where Ω ⊂ R N is a bounded smooth domain, 2 < p < N and a , ψ , φ , f are functions whose properties will be timely introduced. In fact, to obtain our results we will use variational and nonvariational methods, generalizing results already existing in the published literature for the case p = 2 .