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Article Dans Une Revue Communications in Mathematics Année : 2017

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

M.S. Shahrokhi-Dehkordi
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Résumé

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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Dates et versions

hal-03664938 , version 1 (11-05-2022)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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Citer

M.S. Shahrokhi-Dehkordi. On a class of (p; q)-Laplacian problems involving the critical Sobolev-Hardy exponents in starshaped domain. Communications in Mathematics, 2017, Volume 25 (2017), Issue 1 (1), pp.13 - 20. ⟨10.1515/cm-2017-0003⟩. ⟨hal-03664938⟩
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