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

Authors: M.S. Shahrokhi-Dehkordi

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M.S. Shahrokhi-Dehkordi

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.

Aini Zhang;Zhiying Deng, 2022, An existence result for a fractional elliptic system involving (p,q)-Laplacian and critical exponent, Complex Variables and Elliptic Equations, 68, 5, pp. 746-762, 10.1080/17476933.2021.2018424.

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