Biharmonic systems involving multiple Rellich-type potentials and critical Rellich-Sobolev nonlinearities

Dongsheng Kang; Liangshun Xu

doi:10.3934/cpaa.2018019

Article Contents

2018, Volume 17, Issue 2: 333-346. Doi: 10.3934/cpaa.2018019

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Biharmonic systems involving multiple Rellich-type potentials and critical Rellich-Sobolev nonlinearities

Dongsheng Kang^, and
Liangshun Xu

School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China

^* Corresponding author
^* Corresponding author

Received: January 31, 2017

Revised: May 31, 2017

Published: June 2018

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Abstract

In this paper, the minimizers of a Rellich-Sobolev constant are firstly investigated. Secondly, a system of biharmonic equations is investigated, which involves multiple Rellich-type terms and strongly coupled critical Rellich-Sobolev terms. The existence of nontrivial solutions to the system is established by variational arguments.

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Mathematics Subject Classification: Primary:35J60, 31B30;Secondary:35B33, 35B25.

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