A nonlocal elliptic problem on a Heisenberg group

Abstract

We study an elliptic nonlocal problem driven by a source term which is a Radon measure. We prove the existence of a weak solution by a weak convergence method. In the process, we define a new function space which we name the Walker space. The question about the existence of infinitely many nontrivial solutions leads to an interesting conjecture.

References in corpus (6)

• Nonlocal equations with measure data
• On critical variable-order Kirchhoff type problems with variable singular exponent
• Existence and Hölder regularity of infinitely many solutions to a $p$-Kirchhoff type problem involving a singular nonlinearity without the Ambrosetti-Rabinowitz (AR) condition
• Compact Embeddings, Eigenvalue Problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups
• On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group
• On semilinear equations with free boundary conditions on stratified Lie groups