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Multiple nonnegative solutions for BVPs of fourth-order difference equations

Abstract

First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ4x(t-2) = a(t)f(x(t)),t [2, T], x(0) = x(T + 2) = 0, Δ2x(0) = Δ2x(T) = 0 are established by using the well-known Leggett-Williams fixed point theorem, and then, for arbitrary positive integer m, existence results for at least 2m-1 nonnegative solutions are obtained.

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Correspondence to Jian-Ping Sun.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Sun, J. Multiple nonnegative solutions for BVPs of fourth-order difference equations. Adv Differ Equ 2006, 089585 (2006). https://doi.org/10.1155/ADE/2006/89585

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Keywords

  • Differential Equation
  • Positive Integer
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis