Semilinear Elliptic Equation with Biharmonic Operator and Multiple Critical Nonlinearities

Abstract

Abstract We study the existence and non-existence of nontrivial weak solution of , where N ≥ 5, and . Using Pohozaev type of identity, we prove the non-existence result when 1 < q < 2**. On the other hand when the equation has multiple critical nonlinearities i.e. q = 2** and −(N − 2) 2 ≤ μ < μ 1 , we establish the existence of nontrivial solution, using the Mountain-Pass theorem by Ambrosetti and Rabinowitz.