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

摘要

This paper is concerned with the second-order singular Sturm–Liouville integral boundary value problems-u″(t)=λh(t)f(t,u(t)),00,h is allowed to be singular at t=0,1 and f(t,x) may be singular at x=0. By using the 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 non-singular cases.