TY - JOUR
T1 - Existence of solutions to a discrete fourth order boundary value problem
AU - Graef, John R.
AU - Heidarkhani, Shapour
AU - Kong, Lingju
AU - Wang, Min
N1 - Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2018/6/3
Y1 - 2018/6/3
N2 - 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.
AB - 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.
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U2 - 10.1080/10236198.2018.1428963
DO - 10.1080/10236198.2018.1428963
M3 - Article
AN - SCOPUS:85041184993
SN - 1023-6198
VL - 24
SP - 849
EP - 858
JO - Journal of Difference Equations and Applications
JF - Journal of Difference Equations and Applications
IS - 6
ER -