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Communications in Mathematics

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

M.S. Shahrokhi-Dehkordi
Published Online: 2017-06-28 | DOI: https://doi.org/10.1515/cm-2017-0003


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.

Keywords: Quasi-linear elliptic problem; (p; q)-Laplacian operator; Critical Sobolev-Hardy exponent; Starshaped domain


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About the article

Published Online: 2017-06-28

Published in Print: 2017-06-27

Citation Information: Communications in Mathematics, Volume 25, Issue 1, Pages 13–20, ISSN (Online) 2336-1298, DOI: https://doi.org/10.1515/cm-2017-0003.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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