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
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.File in questo prodotto:
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