Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation

Abstract EN

We study the existence of at least one monotonic positive solution for the nonlocal boundary value problem of the second-order functional differential equation x′′(t)=f(t,x(ϕ(t))), t∈(0,1), with the nonlocal condition ∑k=1makx(τk)=x0, x′(0)+∑j=1nbjx′(ηj)=x1, where τk∈(a,d)⊂(0,1), ηj∈(c,e)⊂(0,1), and x0,x1>0.

As an application the integral and the nonlocal conditions ∫adx(t)dt=x0, x′(0)+x(e)-x(c)=x1 will be considered.