Non-trivial solutions for a semilinear biharmonic problem with critical growth and potential vanishing at infinity

Abstract

In this paper, we study the existence of non-trivial solutions for the following class of semilinear biharmonic problem with critical nonlinearity:Here Δ 2u = Δ(Δu), N ≥ 5, μ > 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 variational method, we prove that the problem has at least one non-trivial solution.