On the asymptotic behavior of the eigenvalues of nonlinear elliptic problems in domains becoming unbounded

Abstract

We analyze the asymptotic behavior of the eigenvalues of nonlinear elliptic problems under Dirichlet boundary conditions and mixed (Dirichlet, Neumann) boundary conditions on domains becoming unbounded. We make intensive use of Picone identity to overcome nonlinearity complications. Altogether the use of Picone identity makes the proof easier with respect to the known proof in the linear case. Surprisingly the asymptotic behavior under mixed boundary conditions critically differs from the case of pure Dirichlet boundary conditions for some class of problems.

Study of fractional Poincaré inequalities on unbounded domains

“…Independently, various kinds of problems (mainly PDEs) on Ω have been considered, and their asymptotic behavior as → ∞ is studied. Such kind of theories are now well studied in the local case and for more details on this subject we refer [7], [8], [9], [17], [38] and the references therein.…”