Multiple positive solutions for nonlinear third-order three-point boundary-value problems

Abstract

This paper concerns the nonlinear third-order three-point boundary-value problem$$displaylines{ u'''(t)+h(t)f(u(t))=0, quad tin (0,1), cr u(0)=u'(0)=0, quad u'(1)=alpha u'(eta ),}$$ where $0<eta <1$ and $1<alpha <frac 1eta $. First, we establish the existence of at least three positive solutions by using the well-known Leggett-Williams fixed point theorem. And then, we prove the existence of at least $2m-1$ positive solutions for arbitrary positive integer $m$.

Keywords

• Third-order boundary value problem
• positive solution
• three-point boundary value problem
• existence
• cone
• fixed point