Boundary Value Problems (2018-12-01)

# The continuum branch of positive solutions for discrete simply supported beam equation with local linear growth condition

• Yanqiong Lu,
• Ruyun Ma

DOI
https://doi.org/10.1186/s13661-018-1113-9
Journal volume & issue
Vol. 2018, no. 1
pp. 1 – 14

## Abstract

Abstract In this paper, we obtain the global structure of positive solutions for nonlinear discrete simply supported beam equation Δ4u(t−2)=λf(t,u(t)),t∈T,u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, \begin{aligned}& \Delta ^{4}u(t-2)= \lambda f\bigl(t,u(t)\bigr),\quad t\in \mathbb{T}, \\& u(1)=u(T+1)=\Delta ^{2}u(0)=\Delta ^{2}u(T)=0, \end{aligned} with f∈C(T×[0,∞),[0,∞)) $f\in C(\mathbb{T}\times [0,\infty ),[0,\infty ))$ satisfying local linear growth condition and f(t,0)=0 $f(t,0)=0$ uniformly for t∈T $t\in \mathbb{T}$, where T={2,…,T} $\mathbb{T}=\{2,\ldots,T\}$, λ>0 $\lambda >0$ is a parameter. The main results are based on the global bifurcation theorem.