Existence of positive solutions for a class of discrete problems with ( p,q)-Laplace operators(一类带（p，q）-Laplace算子离散问题正解的存在性)

Abstract

By using the upper and lower solution method, this study proves the existence of positive solutions for a class of discrete problems with （p,q） -Laplace operators-Δ（ϕp（Δut-1））-Δ（ϕq（Δut-1））=λf（ut）, t∈[1,T]Z ,Δu0=uT+1=0,where,λ>0 is a parameter, T>2 is a fixed positive integer,[1,T]Z=1,2,⋯,T, ϕrs=| s | r-2s,Δut=ut+1-ut,f:0,∞→R is p-sublinear at ∞ with possible singularity at 0.(运用上下解方法获得了一类半正离散(p,q) -Laplace问题 -Δ（ϕp（Δut-1））-Δ（ϕq（Δut-1））=λf（ut）, t∈[1,T]Z ,Δu0=uT+1=0正解的存在性，其中，p>q>1，参数λ>0，T>2为固定的整数，[1,T] Z=1,2,⋯,T，ϕrs=| s | r-2s，Δut=ut+1-ut，f :0,∞→R在无穷远处满足p-次线性条件，在0处可能奇异。)

Keywords

• semipositone(半正)
• (p,q)  -laplace(（p,q）-laplace)
• positive solution(正解)
• the upper and lower solution method(上下解方法)