Existence of positive solutions for fourth-order mm-point boundary value problems with a one-dimensional pp-Laplacian operator

This paper discusses the existence of positive solutions for fourth-order mm-point boundary value problems with a one-dimensional pp-Laplacian operator{(ϕp(u″(t)))″−g(t)f(u(t))=0,t∈(0,1),u″(0)=u″(1)=0,au(0)−bu′(0)=∑i=1m−2aiu(ξi),cu(1)+du′(1)=∑i=1m−2biu(ξi), where ϕp(s)=|s|p−2s,p>1,f is a lower semi-continuous function. By using Krasnoselskii’s fixed point theorems in a cone, the existence of one positive solution and multiple positive solutions for nonlinear singular boundary value problems is obtained.