(untitled)
In this paper, by using Krasnoselskii's fixed-point theorem, some sufficient conditions of existence of positive solutions for the following fourth-order nonlinear Sturm-Liouville eigenvalue problem:equation*{arraylll 1p(t)(p(t)u''')'(t)+ λ f(t,u)=0, t(0,1), u(0)=u(1)=0, α u''(0)- β _t → 0^+ p(t)u'''(t)=0, γ u''(1)+δ_t → 1^- p(t)u'''(t)=0, array.equation* are established, where α,β,γ,δ ≥ 0, and βγ+αγ+αδ >0. The function p may be singular at t=0 or 1, and f satisfies Carathéodory condition. , number=4, journal=Journal of Nonlinear Modeling and Analysis, year=2024, month=Apr., pages=485–493