EXISTENCE OF AT LEAST TWO SOLUTIONS OF SECOND ORDER NONLINEAR THREE POINT BOUNDARY VALUE PROBLEMS

摘要

We study existence of solutions of some second order nonlinear three point boundary value problems depending on a parameter of the type -x" = f(t,x,x') - r￠(t), t ∈ (0,1) x(0) = 0, x(1) = δx(η), where η ∈ (0,1) and 0 < δη < 1. We show that for a certain range of the parameter there are no solutions while for some other range of values there are at least two solutions. We use upper and lower solutions and topological degree arguments.