Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities
We study a nonlocal boundary value problem for the equation $x' '(t)+f(t, x(t),x'(t))=0$, $t\in [0,1]$. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume $f\ge 0$. Here the sign of the function $f$ may change.