In this paper,the variational method from local to global is used to generate results of second-order equations to higher-order equations,the existence of solutions for the higher-order Schrödinger equation and Kazdan-Warner equation on locally finite graphs is proved.The existence of rearrangement solutions for a class of nonlinear partial differential equations is proved using the Nehari manifold and rearrangement theory on higher-dimensional lattice graphs.Results of constrained variational problems are generalized to unconstrained variational problems.
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