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

Abstract

In this work, we are interested in the following 1-biharmonic problem with potentials{ε2Δ12u−εΔ1u+V(x)u|u|=K(x)f(u)in RN,u∈BL(RN), where N≥3, ε>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.