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Let $$T > 2$$ T>2 be an integer, $$\mathbb {T}=\{1, 2,\ldots ,T\}$$ T={1,2,…,T} . We are considered with the discrete nonlinear two-point boundary value problem at resonance: $$\begin{aligned} \begin{aligned}&\mathcal {L} u(j)=\nu _1 u(j)+g(u(j))-e(j),\ \ j\in \mathbb {T}, \\&u(0)=u(T+1)=0,&\quad \quad (P)\\ \end{aligned} \end{aligned}$$ Lu(j)=ν1u(j)+g(u(j))-e(j),j∈T,u(0)=u(T+1)=0,(P)...
This paper deals with second-order three-point boundary value problem u''(t)=f(t,u(t)),t (0,1),u(0)=0,u(1)=αu(η),where f:[0,1]xR->R is continuous, α (0,~) and η (0,1) are given constants such that αη=1. We develop the methods of lower and upper solutions by the connectivity properties of the solution set of parameterized families of compact vector fields. As applications of these methods, we...
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