On positive solutions for some second-order three-point boundary value problems with convection term

Abstract

Abstract In this paper, a fixed point theorem in a cone and some inequalities of the associated Green’s function are applied to obtain the existence of positive solutions of second-order three-point boundary value problem with dependence on the first-order derivative x″(t)+f(t,x(t),x′(t))=0,00 $\mu >0$, η∈(0,1) $\eta \in (0, 1)$, μη<1 $\mu \eta <1$. The interesting point is that the nonlinear term is dependent on the convection term.

Keywords

• Three-point boundary value problem
• Fixed point theorem
• Positive solution