Symmetric positive solutions of fourth order boundary value problems for an increasing homeomorphism and homomorphism on time-scales

Let T⊂RT⊂R be a symmetric bounded time-scale, with a=minT,b=maxT. We consider the following fourth order boundary value problem ϕ(−pxΔ∇)Δ∇(t)+f(t,x(t))=0,t∈Tκ2κ2,x(a)=x(b)=0,xΔ∇(σ(a))=xΔ∇(ρ(b))=0 for a suitable function pp and an increasing homeomorphism and homomorphism ϕϕ. By using the Krasnosel’skii fixed point theorem, we present sufficient conditions for the existence of at least one or two symmetric positive solutions of the above problem on time-scales. As applications, two examples are given to illustrate the main results.