Abstract
AbstractLet $T > 1$T>1 be an integer, and let $\mathbb{T}=\{1, 2,\ldots ,T\}$T={1,2,…,T}. We show the existence of positive solutions of the Dirichlet boundary value problem with second-order difference operator
$$ \textstyle\begin{cases} -\triangle ^{2} u(j-1)=\lambda f(j, u(j)), \quad j\in \mathbb{T},\\ u(0)=u(T + 1)=0, \end{cases} $${−△2u(j−1)=λf(j,u(j)),j∈T,u(0)=u(T+1)=0, where $\lambda >0$λ>0 is a parameter, and $f:\mathbb{T}\times \mathbb{R} ^{+}\to \mathbb{R}$f:T×R+→R is a continuous function satisfying $f(j, 0)<0$f(j,0)<0 for all $j\in \mathbb{T}$j∈T. The proofs of the main results are based upon topological degree and global bifurcation techniques.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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