Spectral asymptotics for nonlinear non-autonomous elliptic eigenvalue problems in a ball

Abstract

We consider the following nonlinear elliptic eigenvalue problem

where is and eigenvalue parameter. We treat this problem in the L²-framework and shall establish an asymptotic formula of variational eignevalue where μ_α is a positive solution associated with μ(α). The result is connected with the ground state of the nonlinear scalar field equation.

Keywords:

• Spectral Asymptotics
• Elliptic
• Non-autonomous

Additional information

Notes on contributors

Shibata Tetsutaro