The purpose of this paper is to study the existence of weak solutions for some classes of one--parameter subelliptic gradient--type systems involving a Sobolev--Hardy potential defined on an unbounded domain $Omega_psi$ of the Heisenberg group $mathbb{H}^n=mathbb{C}^n imes mathbb{R}$ ($ngeq 2$) whose geometrical profile is determined by two real positive functions $psi_1$ and $psi_2$ that are bounded on bounded sets. A key ingredient for our variational approach is a very general min--max argument valid for sufficiently smooth functionals defined on reflexive Banach spaces.

Some remarks on gradient-type systems on the Heisenberg group

D'Onofrio L;Molica Bisci G
2019-01-01

Abstract

The purpose of this paper is to study the existence of weak solutions for some classes of one--parameter subelliptic gradient--type systems involving a Sobolev--Hardy potential defined on an unbounded domain $Omega_psi$ of the Heisenberg group $mathbb{H}^n=mathbb{C}^n imes mathbb{R}$ ($ngeq 2$) whose geometrical profile is determined by two real positive functions $psi_1$ and $psi_2$ that are bounded on bounded sets. A key ingredient for our variational approach is a very general min--max argument valid for sufficiently smooth functionals defined on reflexive Banach spaces.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11576/2670569
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