The asymptotic behavior of the first Robin eigenvalue with negative parameter as p goes to +∞

Key Points

• The aim is to explore how the first p-Laplacian eigenvalue behaves as the parameter p becomes very large.
• Investigated the behavior of eigenvalues under Robin boundary conditions
• Analyzed the limit of eigenfunctions as p approaches infinity
• Established conditions for the resultant eigenfunctions to be viscosity solutions
• Proved that the limit of the eigenfunctions is a viscosity solution
• Demonstrated the convergence of the first p-Laplacian eigenvalue under specified conditions