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On a Critical Neumann Problem with a Perturbation of Lower Order

On a Critical Neumann Problem with a Perturbation of Lower Order
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摘要 We investigate the solvability of the Neumann problem （1.1） involving the critical Sobolev nonlinearity and a term of lower order. We allow a coefficient of u in equation （1.1） to be unbounded. We prove the existence of a solution in a weighted Sobolev space. We investigate the solvability of the Neumann problem （1.1） involving the critical Sobolev nonlinearity and a term of lower order. We allow a coefficient of u in equation （1.1） to be unbounded. We prove the existence of a solution in a weighted Sobolev space.
作者 J.Chabrowski
机构地区 Department of Mathematics
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2008年第3期441-452,共12页 应用数学学报（英文版）
关键词 Neumann problem critical Sobolev exponent mountain-pass solutions multiple solutions Neumann problem, critical Sobolev exponent, mountain-pass solutions, multiple solutions
分类号 O175.8 [理学—基础数学]
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参考文献11

  • 1Adimurthi, A., Mancini, G. The Neumann problem for elliptic equations with critical nonlinearity. A tribute in honour of G. Prodi, Scuola Norm. Sup. Pisa 1991,9-25
  • 2Adimurthi, A., Mancini, G. Effect of geometry and topology Of the boundary in critical Neumann problem. J. Reine Angew. Math., 456:1-18 (1994)
  • 3Benci, V. On critical point theory of indefinite functionals in the presence of symmetries. Trans. Amer. Math. Soc., 274:533-572 (1982)
  • 4Brezis, H., Nirenberg, L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Commun. Pure and Appl. Mathematics, ⅩⅩⅩⅣ: 437-477 (1983)
  • 5Cao, D.M., Chabrowski, J. Critical Neumann problem with competing Hardy potentials. Rev. Mat. Complut,, 20:309-338 (2007)
  • 6Chabrowski, J., Willem, M. Least energy solutions of a critical Neumann problem with weight. Calc. Vat., 15:421-431 (2002)
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  • 9Lions, P.L. The concentration - compactness principle in calculus of variations, The Limit Case Ⅰ. Rev. Mat. Iberoamericana, 1:145-201 (1985)
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Acta Mathematicae Applicatae Sinica
2008年 第3期

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