Second-order nonlinear singular Sturm–Liouville problems with integral boundary conditions

This paper is concerned with the second-order singular Sturm–Liouville integral boundary value problems-u″(t)=λh(t)f(t,u(t)),00,hλ>0,h is allowed to be singular at t=0,1t=0,1 and f(t,x)f(t,x) may be singular at x=0x=0. By using the fixed point theory in cones, an explicit interval for λλ is derived such that for any λλ 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 non-singular cases.