Eigenvalues associated with the Khon-Spencer p(•)-biharmonic operator on the Heisenberg group

Abstract

n this study, we consider a nonlinear eigenvalue problem including a Khon-Spencer p(xi )-biharmonic operator under Dirichlet boundary conditions in the Heisenberg group framework. By conducting rigorous analysis, we prove the existence of a positive constant lambda > 0 such that any lambda is an element of (0, lambda), is an eigenvalue for the problem. Our stud-ies relies on variational techniques in the Heisenberg Sobolev space HWk,p(xi )(Omega), where Omega subset of H-n is a Poincare-Sobolev domain.