Using fixed point theorems in ordered Banach spaces with the lattice structure, we consider the existence of nontrivial solutions under the condition that the nonlinear term can change sign and study the existence of sign-changing solutions for some second order three-point boundary value problems. Our results improve and generalize on those in the literatures.
"Existence of Nontrivial Solutions for Unilaterally Asymptotically Linear Three-Point Boundary Value Problems." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/263042