## Abstract

Let Ω ⊂ ℝ^{n} be a bounded starshaped domain and consider the (p; q)-Laplacian problem

-∆_{p}u - ∆_{p}u = λ(x)|u|^{p*-2}u + μ|u|^{r-2}u

where μ is a positive parameter, 1 < q ≤ p < n, r ≥ p* and is the critical Sobolev exponent. In this short note we address the question of non-existence for non-trivial solutions to the (p; q)-Laplacian problem. In particular we show the non-existence of non-trivial solutions to the problem by using a method based on Pohozaev identity.

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