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

M.S. Shahrokhi-Dehkordi

doi:10.1515/cm-2017-0003

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

cm:9461 - Communications in Mathematics, June 28, 2017, Volume 25 (2017), Issue 1 - https://doi.org/10.1515/cm-2017-0003

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

Authors: 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.

https://doi.org/10.1515/cm-2017-0003

Source: HAL:hal-03664938v1

Volume: Volume 25 (2017), Issue 1

Published on: June 28, 2017

Imported on: May 11, 2022

Keywords: [MATH]Mathematics [math]

Licence: Attribution-Non Commercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)