Existence of solutions to a discrete fourth order boundary value problem

John R. Graef, Shapour Heidarkhani, Lingju Kong, Min Wang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Criteria are established for the existence of at least two nontrivial solutions to the discrete fourth order boundary value problem (Formula presented.) where N ≥ 1 is an integer, α,ß ≥ 0 and f : [1, N]Z × R → R is continuous in the second argument. Applications of the results to a related eigenvalue problem are also presented. The proofs are mainly based on the variational method and the classic mountain pass lemma of Ambrosetti and Rabinowitz. Examples are included to illustrate the applicability of the results.

Original languageEnglish (US)
Pages (from-to)849-858
Number of pages10
JournalJournal of Difference Equations and Applications
Volume24
Issue number6
DOIs
StatePublished - Jun 3 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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