Existence and concentration properties for the 1-biharmonic equation with lack of compactness

n this work, we are interested in the following 1-biharmonic problem with potentials � & epsilon;2 & UDelta;2 1u - & epsilon;& UDelta;1u + V(x) u |u| = K(x)f (u) in RN, u & ISIN; BL(RN), where N & GE; 3, & epsilon; > 0 is a positive parameter and V, K, f satisfy some proper conditions. Under the Nehari manifold technique, the Concentration-Compactness Principle and some analysis techniques, we establish the existence and concentration properties of ground state solutions to the 1-biharmonic equation.