TWO NONTRIVIAL SOLUTIONS FOR A DISCRETE FOURTH ORDER PERIODIC BOUNDARY VALUE PROBLEM

TitleTWO NONTRIVIAL SOLUTIONS FOR A DISCRETE FOURTH ORDER PERIODIC BOUNDARY VALUE PROBLEM
Publication TypeJournal Article
Year of Publication2015
AuthorsGraef, JR, KONG, LINGJU, WANG, MIN
Volume19
Issue4
Start Page487
Pagination10
Date Published2015
ISSN1083-2564
AMS34B08, 34B15, 39A10, 58E3
Abstract

We study the discrete fourth order periodic boundary value problem with a parameter $${ \left\{ \begin{array}{1}∆^4u(t − 2) − ∆ \left(p(t − 1)∆_u(t − 1)\right) + q(t)u(t) = λf(t, u(t)), \ t ∈ [1, N]_Z,\\ ∆^iu(−1) = ∆^iu(N − 1), \ \   i = 0, 1, 2, 3.\end{array}\right. }$$ By using variational methods and the mountain pass lemma, sufficient conditions are found under which the above problem has at least two nontrivial solutions. One example is included to illustrate the result.

URLhttp://www.acadsol.eu/en/articles/19/4/1.pdf
Refereed DesignationRefereed
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