| Abstrakt: |
In this paper, we deal with the fractional p (. ,.) -Laplacian problem with nonlocal Neumann boundary conditions { (− Δ) p (. ,.) s u + | u | p ¯ (x) − 2 u = λ V 1 (x) | u | q (x) − 2 u , in Ω , N s , p (. ,.) u = μ V 2 (x) | u | r (x) − 2 u , on R N ∖ Ω , here λ , μ > 0 are parameters and V 1 , V 2 are two nonnegative weighted functions. The domain Ω ⊂ R N (N ≥ 1) is smooth and bounded, p ¯ (x) = p (x , x) , q , r are continuous bounded functions. Applying the Ekeland principle and the variational method, under appropriate assumptions, we show that the above problem has nontrivial weak solutions. [ABSTRACT FROM AUTHOR] |
