We show that a local minimizer of in the topology must be a local minimizer in the topology, under suitable assumptions for the functional with supercritical exponent . This result can be used to establish a solution to the corresponding equation admitting sub- and supersolution. Hence, we extend the conclusion proved by Brezis and Nirenberg (1993), the subcritical and critical case.
Yansheng Zhong. " versus Local Minimizers." Abstr. Appl. Anal. 2014 1 - 6, 2014. https://doi.org/10.1155/2014/646145