Existence of Solutions for Nonlocal p‐Laplacian Equations on Graphs via Intrinsic Operators

ABSTRACT

This paper studies a class of nonlocal ‐Laplacian equations defined on locally finite graphs, where the nonlinearity depends on an intrinsic operator applied to the solution. We develop a functional framework based on discrete Sobolev spaces and establish key properties of the associated operators. Under suitable growth and structural conditions, we prove the existence of weak solutions using pseudomonotone operator theory. Additionally, we derive a priori bounds for solutions and apply our main results to a concrete nonlocal problem involving convolution‐type operators. Our work extends some classical PDE techniques to the graph setting and provides a unified approach for analyzing nonlocal variational problems on discrete structures.