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2014 A Concentration Phenomenon for p-Laplacian Equation
Yansheng Zhong
J. Appl. Math. 2014: 1-6 (2014). DOI: 10.1155/2014/148902


It is proved that if the bounded function of coefficient Qn in the following equation -div{|u|p-2u}+V(x)|u|p-2u=Qn(x)|u|q-2u,u(x)=0asxΩ. u(x)0as|x| is positive in a region contained in Ω and negative outside the region, the sets {Qn>0} shrink to a point x0Ω as n, and then the sequence un generated by the nontrivial solution of the same equation, corresponding to Qn, will concentrate at x0 with respect to W01,p(Ω) and certain Ls(Ω)-norms. In addition, if the sets {Qn>0} shrink to finite points, the corresponding ground states {un} only concentrate at one of these points. These conclusions extend the results proved in the work of Ackermann and Szulkin (2013) for case p=2.


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Yansheng Zhong. "A Concentration Phenomenon for p-Laplacian Equation." J. Appl. Math. 2014 1 - 6, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131355
MathSciNet: MR3246403
Digital Object Identifier: 10.1155/2014/148902

Rights: Copyright © 2014 Hindawi


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