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Infinitely many solutions of a semilinear problem for the Heisenberg Laplacian on the Heisenberg group

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Abstract.

We study the semilinear equation

where is the Heisenberg Laplacian and is the Heisenberg group. The function f ∈ C2(×ℝ, ℝ) is supposed to satisfy some (subcritical) growth conditions and to be left invariant under the action of the subgroup of consisting of points with integer coordinates.. We show the existence of infinitely many solutions in the space S12(), which is the Heisenberg analogue of the Sobolev space W1,2(ℝN).

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  1. Department of Mathematics, University of Virginia Charlottesville, P. O. Box 400137 (Kerchof Hall), VA, 22904-4137, USA

    Sara Maad

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  1. Sara Maad
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Correspondence to Sara Maad.

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Mathematics Subject Classification (2000): 22E30, 22E27

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Maad, S. Infinitely many solutions of a semilinear problem for the Heisenberg Laplacian on the Heisenberg group. manuscripta math. 116, 357–384 (2005). https://doi.org/10.1007/s00229-004-0534-1

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  • DOI: https://doi.org/10.1007/s00229-004-0534-1

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