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Existence of multiple solutions for the Brezis-Nirenberg-type problem with singular coefficients

Yang Yang1*, Jihui Zhang2 and Xiusong Gu3

Author Affiliations

1 School of Science, Jiangnan University, Wuxi, 214122, China

2 School of Mathematical Science, Nanjing Normal University, Nanjing, 210097, China

3 Institute of Science, PLA University of Science and Technology, Nanjing, 211101, China

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Boundary Value Problems 2012, 2012:137  doi:10.1186/1687-2770-2012-137

Published: 26 November 2012


By energy estimates and by establishing a local (PS) condition, we obtain the multiplicity of solutions to a class of Brezis-Nirenberg-type problem with singular coefficients via minimax methods and the Krasnoselskii genus theory.

Brezis-Nirenberg-type problem; minimax method