Ground states solutions for modified fourth-order elliptic systems with steep well potential

In this paper, we study the following modified quasilinear fourth-order elliptic systems { Mathematical Formulas } where ∆² = ∆(∆) is the biharmonic operator, λ 0, and { Mathematical Formulas } is the critical Sobolev exponent for the embedding W 2,2 (R^N) → L ^ 2** (R^N). Under some appropriate assumptions on α(x) and β(x), we obtain that the above problem has nontrivial ground state solutions via the variational methods. We also explore the phenomenon of concentration of solutions.