Let Ω ⊂ ℝn be a bounded starshaped domain and consider the (p; q)-Laplacian problem
-∆pu - ∆pu = λ(x)|u|p*-2u + μ|u|r-2u
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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researchers in the fields of: algebraic structures, calculus of variations, combinatorics, control and optimization, cryptography, differential equations, differential geometry, fuzzy logic and fuzzy set theory, global analysis, mathematical physics and number theory