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Multiple positive solutions to a class of quasi-linear elliptic equations involving critical Sobolev exponent

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Abstract

In this paper, we study the multiplicity results of positive solutions for a quasi-linear problem involving concave-convex nonlinearities and critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem has at least two or three positive solutions under different conditions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Haining Fan & Xiaochun Liu

Authors
  1. Haining Fan
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  2. Xiaochun Liu
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Correspondence to Haining Fan.

Additional information

Communicated by A. Jüngel.

Supported by NSFC (Grant No. 11171261, 11371282).

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Fan, H., Liu, X. Multiple positive solutions to a class of quasi-linear elliptic equations involving critical Sobolev exponent. Monatsh Math 174, 427–447 (2014). https://doi.org/10.1007/s00605-013-0564-4

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