Calculus of variations on locally finite graphs

Yong Lin Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China Yunyan Yang Department of Mathematics, Renmin University of China, Beijing, 100872, China

Analysis of PDEs Combinatorics mathscidoc:2207.03009

Revista Matemática Complutense, 2021.9
Let G=(V,E) be a locally finite graph. Firstly, using calculus of variations, including a direct method of variation and the mountain-pass theory, we get sequences of solutions to several local equations on G (the Schrödinger equation, the mean field equation, and the Yamabe equation). Secondly, we derive uniform estimates for those local solution sequences. Finally, we obtain global solutions by extracting convergent sequence of solutions. Our method can be described as a variational method from local to global.
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  title={Calculus of variations on locally finite graphs},
  author={Yong Lin, and Yunyan Yang},
  booktitle={Revista Matemática Complutense},
Yong Lin, and Yunyan Yang. Calculus of variations on locally finite graphs. 2021. In Revista Matemática Complutense.
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