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A Concentration Phenomenon for p-Laplacian Equation

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  • Yansheng Zhong

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 .

Suggested Citation

  • Yansheng Zhong, 2014. "A Concentration Phenomenon for p-Laplacian Equation," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, July.
    • Handle: RePEc:hin:jnljam:148902
    DOI: 10.1155/2014/148902
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