## Existence of positive solutions of a discrete elastic beam equation.(English)Zbl 1188.39008

Let $$T$$ be an integer with $$T\geq 5$$ and let $$\mathbb T_2=\{2,3,\dots,T\}$$. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equations
$\Delta^4u(t-2)-ra(t)f(u(t))=0,\quad t\in \mathbb T_2,\;u(1)=u(T+1)=\Delta^2u(0)=\Delta^2u(T)=0,$
where $$r$$ is a constant, $$a:\mathbb T_2\to (0,\infty)$$, and $$f:[0,\infty)\to [0,\infty)$$ is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem.

### MSC:

 39A12 Discrete version of topics in analysis 34B15 Nonlinear boundary value problems for ordinary differential equations 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 39A10 Additive difference equations
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### References:

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