Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems

Jianmin Guo and Caixia Guo

Discrete Dynamics in Nature and Society, 2011, vol. 2011, 1-15

Abstract:

By using Morse theory, the critical point theory, and the character of ð ¾ 1 / 2 , we consider the existence and multiplicity results of solutions to the following discrete nonlinear two-point boundary value problem − Δ 2 ð ‘¥ ( 𠑘 − 1 ) = ð ‘“ ( 𠑘 , ð ‘¥ ( 𠑘 ) ) , 𠑘 ∈ ℤ ( 1 , 𠑇 ) subject to ð ‘¥ ( 0 ) = 0 = Δ ð ‘¥ ( 𠑇 ) , where 𠑇 is a positive integer, ℤ ( 1 , 𠑇 ) = { 1 , 2 , … , 𠑇 } , Δ is the forward difference operator defined by Δ ð ‘¥ ( 𠑘 ) = ð ‘¥ ( 𠑘 + 1 ) − ð ‘¥ ( 𠑘 ) , and ð ‘“ ∶ ℤ ( 1 , 𠑇 ) × ℠→ â„ is continuous. In argument, Morse inequalities play an important role.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:319829

DOI: 10.1155/2011/319829

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