Fourth Order Elliptic Equation Involving Sign-Changing Weight Function in RN.

In this paper, we consider the following fourth order elliptic equation Δ 2 u - Δ u + u = κ (x) | u | q - 2 u + | u | p - 2 u , where Δ 2 : = Δ (Δ) is the biharmonic operator, u ∈ H 2 (R N) , N > 4 , 1 < q < 2 < p < 2 ∗ = 2 N N - 4 , and the weight function κ may change sign in R N . By using the Nehari manifold method, we obtain two distinct solutions to this problem under the predefined conditions of κ . [ABSTRACT FROM AUTHOR]