A Concentration Phenomenon for p-Laplacian Equation

Yansheng Zhong

Journal of Applied Mathematics, 2014, vol. 2014, 1-6

Abstract:

It is proved that if the bounded function of coefficient in the following equation   is positive in a region contained in Ω and negative outside the region, the sets shrink to a point as , and then the sequence generated by the nontrivial solution of the same equation, corresponding to , will concentrate at with respect to and certain -norms. In addition, if the sets shrink to finite points, the corresponding ground states only concentrate at one of these points. These conclusions extend the results proved in the work of Ackermann and Szulkin (2013) for case .

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:148902

DOI: 10.1155/2014/148902

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