Existence and iteration of positive solutions for a three-point boundary value problem of second order integro-differential equation with p-Laplace operator

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for the following three-point boundary value problem $$left{begin{array}{l}(phi_p(u'))'(t)+q(t)fleft(u(t),u'(t),Tu(t),Su(t)right)=0,quad0 < t< 1,u'(0)=alpha u'(eta),quad u(1)=g(u'(1)),end{array}right.$$ where ? _p (s)=|s| ^p?2 s,p>1,α∈[0,1),η∈(0,1), T and S are all linear operators, g(t) is continuous and nonincreasing on (?∞,0]. The main tools are monotone iterative technique and numerical simulation. We illustrate our results by one example, and give its numerical results by iterative scheme.