Nonlinear nonhomogeneous Neumann problem on the Heisenberg group

Abstract

Here, the existence of at least one positive radial solution of the Nonlinear nonhomogeneous Neumann problem $-{\mathrm{\Delta }}_{{\mathbb{H}}^n}u+R\left(\xi \right)u=a\left(|\xi {|}_{{\mathbb{H}}^n}\right)\frac{|u{|}^{q-2}u}{1+|u{|}^{q-p}}-b\left(|\xi {|}_{{\mathbb{H}}^n}\right)|u{|}^{q-2}u,\xi \in \mathrm{\Omega }$ is proved on the Heisenberg group ${\mathbb{H}}^n$, via variational principle, where Ω is the Korányi ball, a and b are nonnegative radial functions and $R\left(\xi \right)$ holds in some suitable conditions.

Keywords:

• Heisenberg group
• variational principle
• mountain pass Geometry theorem
• Neumann problem
• Palais–Smale compactness condition
• lie group

2010 Mathematics Subject Classifications:

• 35R03
• 35J20
• 46E35

Disclosure statement

No potential conflict of interest was reported by the author(s).