Eigenvalues of fourth-order singular Sturm–Liouville boundary value problems

In this paper, by establishing a new comparison theorem and constructing upper and lower solutions, some sufficient conditions of existence of positive solutions for the following nonlinear fourth-order singular Sturm–Liouville eigenvalue problem: {1p(t)(p(t)u‴(t))′=λf(t,u),t∈(0,1),u(0)=u(1)=0,αu″(0)−βlimt→0+p(t)u‴(t)=0,γu″(1)+δlimt→1−p(t)u‴(t)=0, are established due to the Schauder’s fixed point theorem for λλ large enough, where α,β,γ,δ≥0,βγ+αγ+αδ>0,f and pp can be singular at t=0t=0 and/or 1; moreover ff can also be singular at u=0u=0. In addition, some peculiar cases are discussed and some further results are obtained.