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# Multiple nonnegative solutions for BVPs of fourth-order difference equations

*Advances in Difference Equations*
**volume 2006**, Article number: 089585 (2006)

## Abstract

First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ^{4}*x*(*t*-2) = *a*(*t*)*f*(*x*(*t*)),*t* ∈ [2, *T*], *x*(0) = *x*(*T* + 2) = 0, Δ^{2}*x*(0) = Δ^{2}*x*(*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 2*m*-1 nonnegative solutions are obtained.

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### Keywords

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