THE p-LAPLACIAN OPERATORS WITH POTENTIAL TERMS

Title & Authors
THE p-LAPLACIAN OPERATORS WITH POTENTIAL TERMS
Chung, Soon-Yeong; Lee, Hee-Soo;

Abstract
In this paper, we deal with the discrete p-Laplacian operators with a potential term having the smallest nonnegative eigenvalue. Such operators are classified as its smallest eigenvalue is positive or zero. We discuss differences between them such as an existence of solutions of p-Laplacian equations on networks and properties of the energy functional. Also, we give some examples of Poisson equations which suggest a difference between linear types and nonlinear types. Finally, we study characteristics of the set of a potential those involving operator has the smallest positive eigenvalue.
Keywords
discrete Laplacian;nonlinear elliptic equations;
Language
English
Cited by
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