Three positive solutions for a nonlinear imageth-order image-point boundary value problem Original Research Article

In this paper, we consider the existence of at least three positive solutions for the nonlinear nnth-order mm-point boundary value problem View the MathML source{u(n)(t)+f(t,u)=0,t∈(0,1),u(0)=0,u′(0)=⋯=u(n−2)(0)=0,u(1)=∑i=1m−2kiu(ξi), Turn MathJax on where View the MathML sourcen≥2,ki>0(i=1,2,…,m−2),0<ξ1<ξ2<⋯<ξm−2<1. The associated Green’s function for the nnth-order mm-point boundary value problem is first given, and growth conditions are imposed on the nonlinearity ff which yield the existence of multiple positive solutions by using the Leggett–Williams fixed point theorem.