Existence of solutions for p-sub-Laplacians with nonlinear sources on the Heisenberg group

Abstract

In this note, we prove the existence of a weak solution for nonlinear p-sub-Laplacian equations with the Dirichlet boundary condition on the Heisenberg group. In the proof, we use a version of the mountain pass theorem and the Folland–Stein embedding theorem as the main tools.

COMMUNICATED BY:

• B. Zhang

Keywords:

• Existence
• p-sub-Laplacian
• mountain pass theorem
• Heisenberg group

AMS SUBJECT CLASSIFICATIONS:

• 35H99
• 35A01
• 22E30

Disclosure statement

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

Additional information

Funding

This work was supported in parts by the Nazarbayev University program 091019CRP2120 and the Nazarbayev University grant 240919FD3901. The first author was also supported in parts by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations and AP08052001 MESRK Grant.