Research article

Existence and multiplicity of nontrivial solutions to discrete elliptic Dirichlet problems


  • Received: 15 April 2022 Revised: 06 May 2022 Accepted: 09 May 2022 Published: 18 May 2022
  • In this paper, we study discrete elliptic Dirichlet problems. Applying a variational technique together with Morse theory, we establish several results on the existence and multiplicity of nontrivial solutions. Finally, two examples and numerical simulations are provided to illustrate our theoretical results.

    Citation: Yuhua Long, Huan Zhang. Existence and multiplicity of nontrivial solutions to discrete elliptic Dirichlet problems[J]. Electronic Research Archive, 2022, 30(7): 2681-2699. doi: 10.3934/era.2022137

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  • In this paper, we study discrete elliptic Dirichlet problems. Applying a variational technique together with Morse theory, we establish several results on the existence and multiplicity of nontrivial solutions. Finally, two examples and numerical simulations are provided to illustrate our theoretical results.



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