LATEX The existence of positive solutions for multi-point BVPs with dependence on the first order derivative

摘要

In this paper, we study the second-order m-point boundary value problem with dependence on the first order derivative x"(t) + f(t,x(t),x''(t)) = 0, 0 leqslant t leqslant 1, x(0) = 0, x(1)-sumlimits_{i = 1}^{m - 2} {k_i xleft( {xi _i } right)} = 0, where k_i ge 0, i = 1,2,...,m-2,0 le xi_1 le xi_2 le cdot cdot cdot le xi_{m-2} le 1. We impose growth conditions on f which yield the existence of at least one positive solution by using a new fixed point theorem.