Positive solutions of fourth-order nonlinear singular Sturm–Liouville eigenvalue problems

We consider the existence of positive solutions for the following fourth-order singular Sturm–Liouville eigenvalue problems{1p(t)(p(t)u‴(t))′−λg(t)F(t,u,u″)=0,00λ>0, g,pg,p may be singular at t=0t=0 and/or 1. Moreover, F(t,x,y)F(t,x,y) may also have singularity at x=0x=0 and/or y=0y=0. By using fixed point theory in cones, an explicit interval for λ is derived such that for any λ in this interval, the existence of at least one positive solution to the boundary value problem is guaranteed. Our results extend and improve many known results including singular and nonsingular cases.