Existence and iteration of positive solution for a three-point boundary value problem with ap-Laplacian operator

摘要

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$left{ begin{gathered} (phi _p (uprime ))prime + q(t)f(t, u) = 0,0< t< 1, hfill u(0) - B(uprime (eta )) = 0, uprime (1) = 0 hfill end{gathered} right.$$ and $$left{ begin{gathered} (phi _p (uprime ))prime + q(t)f(t, u) = 0,0< t< 1, hfill uprime (0) = 0, u(1) + B(uprime (eta )) = 0 hfill end{gathered} right.$$ The main tool is the monotone iterative technique. Here, the coefficientq(t) may be singular att = 0,1.