On a class of (p; q)-Laplacian problems involving the critical Sobolev-Hardy exponents in starshaped domain

Abstract

Let Ω ⊂ R n be a bounded starshaped domain and consider the (p, q)-Laplacian problemwhere µ is a positive parameter, 1 < q ≤ p < n, r ≥ p and p := np n−p 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.