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 < μ1, we establish the existence of nontrivial solution, using the Mountain-Pass theorem by Ambrosetti and Rabinowitz.
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