Existence of three positive solutions to a second-order boundary value problem on a measure chain

Growth conditions are imposed on f such that the boundary value problem −xΔΔ(t)=f(xσ(t)), t∈[t1,t2], λx(t1)−ηxΔ(t1)=0 and μx(σ(t2))+δxΔ(σ(t2))=0, where t1<t2 from a measure chain T, has at least three positive solutions by way of the five functionals fixed point theorem.