Approximation Theorem for Principal Eigenvalue of Discrete $\pmb p$-Laplacian

Abstract

For the principal eigenvalue of discrete weighted $p$-Laplacian on the set of nonnegative integers, the convergence of an approximation procedure and the inverse iteration is proved. Meanwhile, in the proof of the convergence, the monotonicity of an approximation sequence is also checked. To illustrate these results, some examples are presented.