Multiple positive solutions for a second-order boundary value problem with integral boundary conditions

Abstract

In view of the Avery-Peterson fixed point theorem, this paper investigates the existence of three positive solutions for the second-order boundary value problem with integral boundary conditions $$\left \{ \textstyle\begin{array}{@{}l} u''(t)+h(t)f(t,u(t),u'(t))=0,\quad 0< t< 1, u(0)-\alpha u'(0)=\int_{0}^{1}g_{1}(s)u(s)\,ds, u(1)+\beta u'(1)=\int_{0}^{1}g_{2}(s)u(s)\,ds. \end{array}\displaystyle \right . $$ The interesting point is that the nonlinear term involves the first-order derivative explicitly.