In this paper, we study the existence of non-trivial solutions for the following class of semilinear biharmonic problem with critical nonlinearity: Delta(2)u + V (x) u = mu K(x)f(u) + P(x)|u|(2**-2)u, x is an element of R-N, u is an element of D-2,D-2(R-N). Here Delta(2)u = Delta(Delta u), N >= 5, mu > 0 is a parameter, 2** = 2N/(N - 4) is the critical Sobolev exponent, V (x) and K(x) are positive continuous functions that vanish at infinity, f is a function with a subcritical growth and P(x) is a bounded, non-negative continuous function. By working in weighted Sobolev spaces and using a vari...
