Articles

EXISTENCE RESULT FOR A CLASS OF N-LAPLACIAN EQUATIONS INVOLVING CRITICAL GROWTH

  • Guoqing ZHANG ,
  • Weiguo ZHANG ,
  • Sanyang LIU
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  • 1. College of Sciences, University of Shanghai for Science and Technology, Shanghai 200093, China;
    2. College of Mathematics and Statistics, Xidian University, Xi'an 710071, China

Received date: 2016-02-29

  Revised date: 2017-04-28

  Online published: 2017-10-25

Supported by

Supported by Shanghai Natural Science Foundation (15ZR1429500) and NNSF of China (11471215).

Abstract

In this paper,we consider a class of N-Laplacian equations involving critical growth

where Ω is a bounded domain with smooth boundary in RN (N > 2),f (x,u) is of critical growth.Based on the Trudinger-Moser inequality and a nonstandard linking theorem introduced by Degiovanni and Lancelotti,we prove the existence of a nontrivial solution for any λ > λ1,λl=λl(l=2,3,…),and λl is the eigenvalues of the operator (-△N,W01,N(Ω)), which is defined by the Z2-cohomological index.

Cite this article

Guoqing ZHANG , Weiguo ZHANG , Sanyang LIU . EXISTENCE RESULT FOR A CLASS OF N-LAPLACIAN EQUATIONS INVOLVING CRITICAL GROWTH[J]. Acta mathematica scientia, Series B, 2017 , 37(5) : 1348 -1360 . DOI: 10.1016/S0252-9602(17)30077-2

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