Bifurcation from infinity and multiple solutions for some discrete Sturm–Liouville problems

In this paper, we study nonlinear discrete boundary value problems of the form Δ[p(t−1)Δy(t−1)]+q(t)y(t)+(λk+λ)y(t)+f(t,y(t))=h(t),t∈T,a11y(a)+a12Δy(a)=0,a21y(b+1)+a22Δy(b+1)=0, where λkλk is an eigenvalue of the associated linear problem, λλ is a parameter, and ff satisfies the sublinear growth condition |f(t,s)|≤A|s|α+B,t∈{a+1,…,b+1},s∈R for some 0≤α<10≤α<1 and A,B∈(0,∞)A,B∈(0,∞). We study the existence and multiplicity of solutions for the above-mentioned problems by establishing some a priori bounds, together with Leray–Schauder continuation and bifurcation arguments.