Opuscula Math. 33, no. 2 (2013), 237-354
http://dx.doi.org/10.7494/OpMath.2013.33.2.237

 
Opuscula Mathematica

Existence of solution of sub-elliptic equations on the Heisenberg group with critical growth and double singularities

Jianqing Chen
Eugénio M. Rocha

Abstract. For a class of sub-elliptic equations on Heisenberg group \(\mathbb{H}^N\) with Hardy type singularity and critical nonlinear growth, we prove the existence of least energy solutions by developing new techniques based on the Nehari constraint. This result extends previous works, e.g., by Han et al. [Hardy-Sobolev type inequalities on the H-type group, Manuscripta Math. 118 (2005), 235–252].

Keywords: sub-elliptic equations, Heisenberg group, Least energy solutions.

Mathematics Subject Classification: 35H20, 35J60.

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  • Jianqing Chen
  • University of Aveiro, Department of Mathematics and CIDMA-Center for Research and Development in Mathematics and Applications, 3810-193 Aveiro, Portugal
  • Eugénio M. Rocha
  • University of Aveiro, Department of Mathematics and CIDMA-Center for Research and Development in Mathematics and Applications, 3810-193 Aveiro, Portugal
  • Received: 2012-12-04.
  • Accepted: 2012-12-08.
Opuscula Mathematica - cover

Cite this article as:
Jianqing Chen, Eugénio M. Rocha, Existence of solution of sub-elliptic equations on the Heisenberg group with critical growth and double singularities, Opuscula Math. 33, no. 2 (2013), 237-354, http://dx.doi.org/10.7494/OpMath.2013.33.2.237

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