Liouville theorems for semilinear equations on the Heisenberg group

Abstract

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Entire solutions of quasilinear elliptic systems on Carnot groups

“…Earlier contributions on the nonexistence question for semilinear scalar subelliptic problems with power nonlinearities were obtained by Capuzzo-Dolcetta and Cutrì [6], Birindelli, Capuzzo-Dolcetta and Cutrì [3]. The quasilinear case was studied by D'Ambrosio [9].…”

Liouville type theorem for nonlinear boundary value problem on Heisenberg group

“…For example, in the paper [1], the authors considered the following elliptic inequality on the Heisenberg group H n (1.1)…”

“…After the work of [1], there are plenty of works concerning on the nonexistence results for the following elliptic equation rather than elliptic inequality (1.2) ∆ H u + u p = 0 in H n .…”

Liouville theorems for fully nonlinear elliptic equations on spherically symmetric Riemannian manifolds

“…Let us mention that Liouville theorems have been also established on the Heisenberg group for semilinear elliptic equations (see [2]). …”