Positive Solutions for a nonlinear n-th order m-point boundary-value problem

Abstract

Using the Leggett-Williams fixed point theorem in cones, we prove the existence of at least three positive solutions to the nonlinear $n$-th order $m$-point boundary-value problem $$displaylines{ Delta^{n}u(k)+a(k)f(k,u)=0, quad kin {0,N},cr u(0)=0,; Delta u(0)=0, dots, Delta^{n-2}u(0)=0,quad u(N+n)=sum_{i=1}^{m-2}alpha_iu(xi_i). }$$

Keywords

• Boundary value problem
• positive solution
• fixed point theorem
• Green's function