Positive solutions of fourth-order four-point boundary value problems with p-Laplacian operator

In this paper, we consider the existence of positive solutions for the singular fourth-order p-Laplacian equation[φp(u″(t))]″=f(t,u(t)),01p>1, 0<ξ,η<10<ξ,η<1, f∈C((0,1)×(0,+∞),[0,+∞))f∈C((0,1)×(0,+∞),[0,+∞)) may be singular at t=0t=0 and/or 1 and u=0u=0. By using the upper and lower solution method and fixed-point theorems, the existence of positive solutions to the above the boundary value problem is obtained.