On a discrete fourth order periodic boundary value problem

John R. Graef; Lingju Kong; Y. U. Tian; Min Wang

On a discrete fourth order periodic boundary value problem

John R. Graef, Lingju Kong, Y. U. Tian, Min Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The authors study the discrete fourth order periodic boundary value problem (Lu)(t) = λf(t,u(t)) + μg(t,u(t)), t∈[1,N]z, Δⁱu(-1) = Δⁱu(N - 1), 1 = 0, 1, 2, 3, where (Lu)(t) = Δ⁴u(t - 2) - Δ(p(t - 1)Δu(t - 1)) + q(t)u(t). By using variational methods and critical point theory, they obtain some criteria for the existence of infinitely many solutions. Several consequences of the main theorems are also presented. One example is included to illustrate the applicability of the results.

Original language	English (US)
Pages (from-to)	163-184
Number of pages	22
Journal	Indian Journal of Mathematics
Volume	55
Issue number	2
State	Published - Aug 1 2013

All Science Journal Classification (ASJC) codes

Mathematics(all)

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title = "On a discrete fourth order periodic boundary value problem",

abstract = "The authors study the discrete fourth order periodic boundary value problem (Lu)(t) = λf(t,u(t)) + μg(t,u(t)), t∈[1,N]z, Δiu(-1) = Δiu(N - 1), 1 = 0, 1, 2, 3, where (Lu)(t) = Δ4u(t - 2) - Δ(p(t - 1)Δu(t - 1)) + q(t)u(t). By using variational methods and critical point theory, they obtain some criteria for the existence of infinitely many solutions. Several consequences of the main theorems are also presented. One example is included to illustrate the applicability of the results.",

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T1 - On a discrete fourth order periodic boundary value problem

AU - Graef, John R.

AU - Kong, Lingju

AU - Tian, Y. U.

AU - Wang, Min

PY - 2013/8/1

Y1 - 2013/8/1

N2 - The authors study the discrete fourth order periodic boundary value problem (Lu)(t) = λf(t,u(t)) + μg(t,u(t)), t∈[1,N]z, Δiu(-1) = Δiu(N - 1), 1 = 0, 1, 2, 3, where (Lu)(t) = Δ4u(t - 2) - Δ(p(t - 1)Δu(t - 1)) + q(t)u(t). By using variational methods and critical point theory, they obtain some criteria for the existence of infinitely many solutions. Several consequences of the main theorems are also presented. One example is included to illustrate the applicability of the results.

AB - The authors study the discrete fourth order periodic boundary value problem (Lu)(t) = λf(t,u(t)) + μg(t,u(t)), t∈[1,N]z, Δiu(-1) = Δiu(N - 1), 1 = 0, 1, 2, 3, where (Lu)(t) = Δ4u(t - 2) - Δ(p(t - 1)Δu(t - 1)) + q(t)u(t). By using variational methods and critical point theory, they obtain some criteria for the existence of infinitely many solutions. Several consequences of the main theorems are also presented. One example is included to illustrate the applicability of the results.

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M3 - Article

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VL - 55

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EP - 184

JO - Indian Journal of Mathematics

JF - Indian Journal of Mathematics

SN - 0019-5324

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ER -